Zero-viscosity-capillarity limit to the planar rarefaction wave for the 2D compressible Navier–Stokes–Korteweg equations
We shall consider the two-dimensional (2D) isentropic Navier–Stokes–Korteweg equations which are used to model compressible fluids with internal capillarity. Formally, the 2D isentropic Navier–Stokes–Korteweg equations converge, as the viscosity and the capillarity vanish, to the corresponding 2D in...
Ausführliche Beschreibung
Autor*in: |
Yin, Rong [verfasserIn] Li, Yeping [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2022 |
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Schlagwörter: |
Compressible Navier–Stokes–Korteweg equations |
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Übergeordnetes Werk: |
Enthalten in: Nonlinear analysis / Real world applications - Amsterdam [u.a.] : Elsevier Science, 2000, 68 |
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Übergeordnetes Werk: |
volume:68 |
DOI / URN: |
10.1016/j.nonrwa.2022.103685 |
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Katalog-ID: |
ELV008284725 |
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245 | 1 | 0 | |a Zero-viscosity-capillarity limit to the planar rarefaction wave for the 2D compressible Navier–Stokes–Korteweg equations |
264 | 1 | |c 2022 | |
336 | |a nicht spezifiziert |b zzz |2 rdacontent | ||
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520 | |a We shall consider the two-dimensional (2D) isentropic Navier–Stokes–Korteweg equations which are used to model compressible fluids with internal capillarity. Formally, the 2D isentropic Navier–Stokes–Korteweg equations converge, as the viscosity and the capillarity vanish, to the corresponding 2D inviscid Euler equations, and we do justify this for the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. More precisely, it is proved that there exists a family of smooth solutions for the 2D isentropic compressible Navier–Stokes–Korteweg equations converging to the planar rarefaction wave solution with arbitrary strength for the 2D Euler equations. A uniform convergence rate is obtained in terms of the viscosity coefficient and the capillarity away from the initial time. The key ingredients of our proof are the re-scaling technique and energy estimate, in which we also introduce the hyperbolic wave to recover the physical viscosities and capillarity of the inviscid rarefaction wave profile. | ||
650 | 4 | |a Planar rarefaction wave | |
650 | 4 | |a Compressible Navier–Stokes–Korteweg equations | |
650 | 4 | |a Zero-viscosity-capillarity limit | |
650 | 4 | |a Energy estimate | |
700 | 1 | |a Li, Yeping |e verfasserin |4 aut | |
773 | 0 | 8 | |i Enthalten in |t Nonlinear analysis / Real world applications |d Amsterdam [u.a.] : Elsevier Science, 2000 |g 68 |h Online-Ressource |w (DE-627)336799039 |w (DE-600)2061967-4 |w (DE-576)099718286 |7 nnns |
773 | 1 | 8 | |g volume:68 |
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936 | b | k | |a 31.55 |j Globale Analysis |
936 | b | k | |a 31.46 |j Funktionalanalysis |
951 | |a AR | ||
952 | |d 68 |
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r y ry y l yl |
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yinrongliyeping:2022----:eoicstcplaiyiittelnraeatowvfrh2cmrsilnv |
hierarchy_sort_str |
2022 |
bklnumber |
31.55 31.46 |
publishDate |
2022 |
allfields |
10.1016/j.nonrwa.2022.103685 doi (DE-627)ELV008284725 (ELSEVIER)S1468-1218(22)00099-2 DE-627 ger DE-627 rda eng 510 DE-600 31.55 bkl 31.46 bkl Yin, Rong verfasserin aut Zero-viscosity-capillarity limit to the planar rarefaction wave for the 2D compressible Navier–Stokes–Korteweg equations 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We shall consider the two-dimensional (2D) isentropic Navier–Stokes–Korteweg equations which are used to model compressible fluids with internal capillarity. Formally, the 2D isentropic Navier–Stokes–Korteweg equations converge, as the viscosity and the capillarity vanish, to the corresponding 2D inviscid Euler equations, and we do justify this for the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. More precisely, it is proved that there exists a family of smooth solutions for the 2D isentropic compressible Navier–Stokes–Korteweg equations converging to the planar rarefaction wave solution with arbitrary strength for the 2D Euler equations. A uniform convergence rate is obtained in terms of the viscosity coefficient and the capillarity away from the initial time. The key ingredients of our proof are the re-scaling technique and energy estimate, in which we also introduce the hyperbolic wave to recover the physical viscosities and capillarity of the inviscid rarefaction wave profile. Planar rarefaction wave Compressible Navier–Stokes–Korteweg equations Zero-viscosity-capillarity limit Energy estimate Li, Yeping verfasserin aut Enthalten in Nonlinear analysis / Real world applications Amsterdam [u.a.] : Elsevier Science, 2000 68 Online-Ressource (DE-627)336799039 (DE-600)2061967-4 (DE-576)099718286 nnns volume:68 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.55 Globale Analysis 31.46 Funktionalanalysis AR 68 |
spelling |
10.1016/j.nonrwa.2022.103685 doi (DE-627)ELV008284725 (ELSEVIER)S1468-1218(22)00099-2 DE-627 ger DE-627 rda eng 510 DE-600 31.55 bkl 31.46 bkl Yin, Rong verfasserin aut Zero-viscosity-capillarity limit to the planar rarefaction wave for the 2D compressible Navier–Stokes–Korteweg equations 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We shall consider the two-dimensional (2D) isentropic Navier–Stokes–Korteweg equations which are used to model compressible fluids with internal capillarity. Formally, the 2D isentropic Navier–Stokes–Korteweg equations converge, as the viscosity and the capillarity vanish, to the corresponding 2D inviscid Euler equations, and we do justify this for the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. More precisely, it is proved that there exists a family of smooth solutions for the 2D isentropic compressible Navier–Stokes–Korteweg equations converging to the planar rarefaction wave solution with arbitrary strength for the 2D Euler equations. A uniform convergence rate is obtained in terms of the viscosity coefficient and the capillarity away from the initial time. The key ingredients of our proof are the re-scaling technique and energy estimate, in which we also introduce the hyperbolic wave to recover the physical viscosities and capillarity of the inviscid rarefaction wave profile. Planar rarefaction wave Compressible Navier–Stokes–Korteweg equations Zero-viscosity-capillarity limit Energy estimate Li, Yeping verfasserin aut Enthalten in Nonlinear analysis / Real world applications Amsterdam [u.a.] : Elsevier Science, 2000 68 Online-Ressource (DE-627)336799039 (DE-600)2061967-4 (DE-576)099718286 nnns volume:68 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.55 Globale Analysis 31.46 Funktionalanalysis AR 68 |
allfields_unstemmed |
10.1016/j.nonrwa.2022.103685 doi (DE-627)ELV008284725 (ELSEVIER)S1468-1218(22)00099-2 DE-627 ger DE-627 rda eng 510 DE-600 31.55 bkl 31.46 bkl Yin, Rong verfasserin aut Zero-viscosity-capillarity limit to the planar rarefaction wave for the 2D compressible Navier–Stokes–Korteweg equations 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We shall consider the two-dimensional (2D) isentropic Navier–Stokes–Korteweg equations which are used to model compressible fluids with internal capillarity. Formally, the 2D isentropic Navier–Stokes–Korteweg equations converge, as the viscosity and the capillarity vanish, to the corresponding 2D inviscid Euler equations, and we do justify this for the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. More precisely, it is proved that there exists a family of smooth solutions for the 2D isentropic compressible Navier–Stokes–Korteweg equations converging to the planar rarefaction wave solution with arbitrary strength for the 2D Euler equations. A uniform convergence rate is obtained in terms of the viscosity coefficient and the capillarity away from the initial time. The key ingredients of our proof are the re-scaling technique and energy estimate, in which we also introduce the hyperbolic wave to recover the physical viscosities and capillarity of the inviscid rarefaction wave profile. Planar rarefaction wave Compressible Navier–Stokes–Korteweg equations Zero-viscosity-capillarity limit Energy estimate Li, Yeping verfasserin aut Enthalten in Nonlinear analysis / Real world applications Amsterdam [u.a.] : Elsevier Science, 2000 68 Online-Ressource (DE-627)336799039 (DE-600)2061967-4 (DE-576)099718286 nnns volume:68 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.55 Globale Analysis 31.46 Funktionalanalysis AR 68 |
allfieldsGer |
10.1016/j.nonrwa.2022.103685 doi (DE-627)ELV008284725 (ELSEVIER)S1468-1218(22)00099-2 DE-627 ger DE-627 rda eng 510 DE-600 31.55 bkl 31.46 bkl Yin, Rong verfasserin aut Zero-viscosity-capillarity limit to the planar rarefaction wave for the 2D compressible Navier–Stokes–Korteweg equations 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We shall consider the two-dimensional (2D) isentropic Navier–Stokes–Korteweg equations which are used to model compressible fluids with internal capillarity. Formally, the 2D isentropic Navier–Stokes–Korteweg equations converge, as the viscosity and the capillarity vanish, to the corresponding 2D inviscid Euler equations, and we do justify this for the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. More precisely, it is proved that there exists a family of smooth solutions for the 2D isentropic compressible Navier–Stokes–Korteweg equations converging to the planar rarefaction wave solution with arbitrary strength for the 2D Euler equations. A uniform convergence rate is obtained in terms of the viscosity coefficient and the capillarity away from the initial time. The key ingredients of our proof are the re-scaling technique and energy estimate, in which we also introduce the hyperbolic wave to recover the physical viscosities and capillarity of the inviscid rarefaction wave profile. Planar rarefaction wave Compressible Navier–Stokes–Korteweg equations Zero-viscosity-capillarity limit Energy estimate Li, Yeping verfasserin aut Enthalten in Nonlinear analysis / Real world applications Amsterdam [u.a.] : Elsevier Science, 2000 68 Online-Ressource (DE-627)336799039 (DE-600)2061967-4 (DE-576)099718286 nnns volume:68 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.55 Globale Analysis 31.46 Funktionalanalysis AR 68 |
allfieldsSound |
10.1016/j.nonrwa.2022.103685 doi (DE-627)ELV008284725 (ELSEVIER)S1468-1218(22)00099-2 DE-627 ger DE-627 rda eng 510 DE-600 31.55 bkl 31.46 bkl Yin, Rong verfasserin aut Zero-viscosity-capillarity limit to the planar rarefaction wave for the 2D compressible Navier–Stokes–Korteweg equations 2022 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We shall consider the two-dimensional (2D) isentropic Navier–Stokes–Korteweg equations which are used to model compressible fluids with internal capillarity. Formally, the 2D isentropic Navier–Stokes–Korteweg equations converge, as the viscosity and the capillarity vanish, to the corresponding 2D inviscid Euler equations, and we do justify this for the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. More precisely, it is proved that there exists a family of smooth solutions for the 2D isentropic compressible Navier–Stokes–Korteweg equations converging to the planar rarefaction wave solution with arbitrary strength for the 2D Euler equations. A uniform convergence rate is obtained in terms of the viscosity coefficient and the capillarity away from the initial time. The key ingredients of our proof are the re-scaling technique and energy estimate, in which we also introduce the hyperbolic wave to recover the physical viscosities and capillarity of the inviscid rarefaction wave profile. Planar rarefaction wave Compressible Navier–Stokes–Korteweg equations Zero-viscosity-capillarity limit Energy estimate Li, Yeping verfasserin aut Enthalten in Nonlinear analysis / Real world applications Amsterdam [u.a.] : Elsevier Science, 2000 68 Online-Ressource (DE-627)336799039 (DE-600)2061967-4 (DE-576)099718286 nnns volume:68 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.55 Globale Analysis 31.46 Funktionalanalysis AR 68 |
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Zero-viscosity-capillarity limit to the planar rarefaction wave for the 2D compressible Navier–Stokes–Korteweg equations |
ctrlnum |
(DE-627)ELV008284725 (ELSEVIER)S1468-1218(22)00099-2 |
title_full |
Zero-viscosity-capillarity limit to the planar rarefaction wave for the 2D compressible Navier–Stokes–Korteweg equations |
author_sort |
Yin, Rong |
journal |
Nonlinear analysis / Real world applications |
journalStr |
Nonlinear analysis / Real world applications |
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eng |
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500 - Science |
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2022 |
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zzz |
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Yin, Rong Li, Yeping |
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68 |
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format_se |
Elektronische Aufsätze |
author-letter |
Yin, Rong |
doi_str_mv |
10.1016/j.nonrwa.2022.103685 |
dewey-full |
510 |
author2-role |
verfasserin |
title_sort |
zero-viscosity-capillarity limit to the planar rarefaction wave for the 2d compressible navier–stokes–korteweg equations |
title_auth |
Zero-viscosity-capillarity limit to the planar rarefaction wave for the 2D compressible Navier–Stokes–Korteweg equations |
abstract |
We shall consider the two-dimensional (2D) isentropic Navier–Stokes–Korteweg equations which are used to model compressible fluids with internal capillarity. Formally, the 2D isentropic Navier–Stokes–Korteweg equations converge, as the viscosity and the capillarity vanish, to the corresponding 2D inviscid Euler equations, and we do justify this for the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. More precisely, it is proved that there exists a family of smooth solutions for the 2D isentropic compressible Navier–Stokes–Korteweg equations converging to the planar rarefaction wave solution with arbitrary strength for the 2D Euler equations. A uniform convergence rate is obtained in terms of the viscosity coefficient and the capillarity away from the initial time. The key ingredients of our proof are the re-scaling technique and energy estimate, in which we also introduce the hyperbolic wave to recover the physical viscosities and capillarity of the inviscid rarefaction wave profile. |
abstractGer |
We shall consider the two-dimensional (2D) isentropic Navier–Stokes–Korteweg equations which are used to model compressible fluids with internal capillarity. Formally, the 2D isentropic Navier–Stokes–Korteweg equations converge, as the viscosity and the capillarity vanish, to the corresponding 2D inviscid Euler equations, and we do justify this for the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. More precisely, it is proved that there exists a family of smooth solutions for the 2D isentropic compressible Navier–Stokes–Korteweg equations converging to the planar rarefaction wave solution with arbitrary strength for the 2D Euler equations. A uniform convergence rate is obtained in terms of the viscosity coefficient and the capillarity away from the initial time. The key ingredients of our proof are the re-scaling technique and energy estimate, in which we also introduce the hyperbolic wave to recover the physical viscosities and capillarity of the inviscid rarefaction wave profile. |
abstract_unstemmed |
We shall consider the two-dimensional (2D) isentropic Navier–Stokes–Korteweg equations which are used to model compressible fluids with internal capillarity. Formally, the 2D isentropic Navier–Stokes–Korteweg equations converge, as the viscosity and the capillarity vanish, to the corresponding 2D inviscid Euler equations, and we do justify this for the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. More precisely, it is proved that there exists a family of smooth solutions for the 2D isentropic compressible Navier–Stokes–Korteweg equations converging to the planar rarefaction wave solution with arbitrary strength for the 2D Euler equations. A uniform convergence rate is obtained in terms of the viscosity coefficient and the capillarity away from the initial time. The key ingredients of our proof are the re-scaling technique and energy estimate, in which we also introduce the hyperbolic wave to recover the physical viscosities and capillarity of the inviscid rarefaction wave profile. |
collection_details |
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title_short |
Zero-viscosity-capillarity limit to the planar rarefaction wave for the 2D compressible Navier–Stokes–Korteweg equations |
remote_bool |
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author2 |
Li, Yeping |
author2Str |
Li, Yeping |
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doi_str |
10.1016/j.nonrwa.2022.103685 |
up_date |
2024-07-06T19:10:33.146Z |
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