Liouville theorems for the Navier–Stokes equations and applications

Abstract We study bounded ancient solutions of the Navier–Stokes equations. These are solutions with bounded velocity defined in Rn × (−1, 0). In two space dimensions we prove that such solutions are either constant or of the form u(x, t) = b(t), depending on the exact definition of admissible solut...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Koch, Gabriel [verfasserIn] Nadirashvili, Nikolai Seregin, Gregory A. Šverák, Vladimir

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2009

Schlagwörter:	Weak Solution Cauchy Problem Stokes Equation Mild Solution Harnack Inequality

Anmerkung:	© Institut Mittag-Leffler 2009

Übergeordnetes Werk:	Enthalten in: Acta mathematica - Somerville, Mass. : International Press, 1882, 203(2009), 1 vom: Sept., Seite 83-105
Übergeordnetes Werk:	volume:203 ; year:2009 ; number:1 ; month:09 ; pages:83-105

Links:	Volltext

DOI / URN:	10.1007/s11511-009-0039-6

Katalog-ID:	SPR020477570

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520			\|a Abstract We study bounded ancient solutions of the Navier–Stokes equations. These are solutions with bounded velocity defined in Rn × (−1, 0). In two space dimensions we prove that such solutions are either constant or of the form u(x, t) = b(t), depending on the exact definition of admissible solutions. The general 3-dimensional problem seems to be out of reach of existing techniques, but partial results can be obtained in the case of axisymmetric solutions. We apply these results to some scenarios of potential singularity formation for axi-symmetric solutions, and obtain extensions of results in a recent paper by Chen, Strain, Tsai and Yau [4].
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650		4	\|a Mild Solution \|7 (dpeaa)DE-He213
650		4	\|a Harnack Inequality \|7 (dpeaa)DE-He213
700	1		\|a Nadirashvili, Nikolai \|4 aut
700	1		\|a Seregin, Gregory A. \|4 aut
700	1		\|a Šverák, Vladimir \|4 aut
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951			\|a AR
952			\|d 203 \|j 2009 \|e 1 \|c 09 \|h 83-105

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allfields	10.1007/s11511-009-0039-6 doi (DE-627)SPR020477570 (SPR)s11511-009-0039-6-e DE-627 ger DE-627 rakwb eng Koch, Gabriel verfasserin aut Liouville theorems for the Navier–Stokes equations and applications 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institut Mittag-Leffler 2009 Abstract We study bounded ancient solutions of the Navier–Stokes equations. These are solutions with bounded velocity defined in Rn × (−1, 0). In two space dimensions we prove that such solutions are either constant or of the form u(x, t) = b(t), depending on the exact definition of admissible solutions. The general 3-dimensional problem seems to be out of reach of existing techniques, but partial results can be obtained in the case of axisymmetric solutions. We apply these results to some scenarios of potential singularity formation for axi-symmetric solutions, and obtain extensions of results in a recent paper by Chen, Strain, Tsai and Yau [4]. Weak Solution (dpeaa)DE-He213 Cauchy Problem (dpeaa)DE-He213 Stokes Equation (dpeaa)DE-He213 Mild Solution (dpeaa)DE-He213 Harnack Inequality (dpeaa)DE-He213 Nadirashvili, Nikolai aut Seregin, Gregory A. aut Šverák, Vladimir aut Enthalten in Acta mathematica Somerville, Mass. : International Press, 1882 203(2009), 1 vom: Sept., Seite 83-105 (DE-627)364462922 (DE-600)2109566-8 1871-2509 nnns volume:203 year:2009 number:1 month:09 pages:83-105 https://dx.doi.org/10.1007/s11511-009-0039-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 203 2009 1 09 83-105
spelling	10.1007/s11511-009-0039-6 doi (DE-627)SPR020477570 (SPR)s11511-009-0039-6-e DE-627 ger DE-627 rakwb eng Koch, Gabriel verfasserin aut Liouville theorems for the Navier–Stokes equations and applications 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institut Mittag-Leffler 2009 Abstract We study bounded ancient solutions of the Navier–Stokes equations. These are solutions with bounded velocity defined in Rn × (−1, 0). In two space dimensions we prove that such solutions are either constant or of the form u(x, t) = b(t), depending on the exact definition of admissible solutions. The general 3-dimensional problem seems to be out of reach of existing techniques, but partial results can be obtained in the case of axisymmetric solutions. We apply these results to some scenarios of potential singularity formation for axi-symmetric solutions, and obtain extensions of results in a recent paper by Chen, Strain, Tsai and Yau [4]. Weak Solution (dpeaa)DE-He213 Cauchy Problem (dpeaa)DE-He213 Stokes Equation (dpeaa)DE-He213 Mild Solution (dpeaa)DE-He213 Harnack Inequality (dpeaa)DE-He213 Nadirashvili, Nikolai aut Seregin, Gregory A. aut Šverák, Vladimir aut Enthalten in Acta mathematica Somerville, Mass. : International Press, 1882 203(2009), 1 vom: Sept., Seite 83-105 (DE-627)364462922 (DE-600)2109566-8 1871-2509 nnns volume:203 year:2009 number:1 month:09 pages:83-105 https://dx.doi.org/10.1007/s11511-009-0039-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 203 2009 1 09 83-105
allfields_unstemmed	10.1007/s11511-009-0039-6 doi (DE-627)SPR020477570 (SPR)s11511-009-0039-6-e DE-627 ger DE-627 rakwb eng Koch, Gabriel verfasserin aut Liouville theorems for the Navier–Stokes equations and applications 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institut Mittag-Leffler 2009 Abstract We study bounded ancient solutions of the Navier–Stokes equations. These are solutions with bounded velocity defined in Rn × (−1, 0). In two space dimensions we prove that such solutions are either constant or of the form u(x, t) = b(t), depending on the exact definition of admissible solutions. The general 3-dimensional problem seems to be out of reach of existing techniques, but partial results can be obtained in the case of axisymmetric solutions. We apply these results to some scenarios of potential singularity formation for axi-symmetric solutions, and obtain extensions of results in a recent paper by Chen, Strain, Tsai and Yau [4]. Weak Solution (dpeaa)DE-He213 Cauchy Problem (dpeaa)DE-He213 Stokes Equation (dpeaa)DE-He213 Mild Solution (dpeaa)DE-He213 Harnack Inequality (dpeaa)DE-He213 Nadirashvili, Nikolai aut Seregin, Gregory A. aut Šverák, Vladimir aut Enthalten in Acta mathematica Somerville, Mass. : International Press, 1882 203(2009), 1 vom: Sept., Seite 83-105 (DE-627)364462922 (DE-600)2109566-8 1871-2509 nnns volume:203 year:2009 number:1 month:09 pages:83-105 https://dx.doi.org/10.1007/s11511-009-0039-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 203 2009 1 09 83-105
allfieldsGer	10.1007/s11511-009-0039-6 doi (DE-627)SPR020477570 (SPR)s11511-009-0039-6-e DE-627 ger DE-627 rakwb eng Koch, Gabriel verfasserin aut Liouville theorems for the Navier–Stokes equations and applications 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institut Mittag-Leffler 2009 Abstract We study bounded ancient solutions of the Navier–Stokes equations. These are solutions with bounded velocity defined in Rn × (−1, 0). In two space dimensions we prove that such solutions are either constant or of the form u(x, t) = b(t), depending on the exact definition of admissible solutions. The general 3-dimensional problem seems to be out of reach of existing techniques, but partial results can be obtained in the case of axisymmetric solutions. We apply these results to some scenarios of potential singularity formation for axi-symmetric solutions, and obtain extensions of results in a recent paper by Chen, Strain, Tsai and Yau [4]. Weak Solution (dpeaa)DE-He213 Cauchy Problem (dpeaa)DE-He213 Stokes Equation (dpeaa)DE-He213 Mild Solution (dpeaa)DE-He213 Harnack Inequality (dpeaa)DE-He213 Nadirashvili, Nikolai aut Seregin, Gregory A. aut Šverák, Vladimir aut Enthalten in Acta mathematica Somerville, Mass. : International Press, 1882 203(2009), 1 vom: Sept., Seite 83-105 (DE-627)364462922 (DE-600)2109566-8 1871-2509 nnns volume:203 year:2009 number:1 month:09 pages:83-105 https://dx.doi.org/10.1007/s11511-009-0039-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 203 2009 1 09 83-105
allfieldsSound	10.1007/s11511-009-0039-6 doi (DE-627)SPR020477570 (SPR)s11511-009-0039-6-e DE-627 ger DE-627 rakwb eng Koch, Gabriel verfasserin aut Liouville theorems for the Navier–Stokes equations and applications 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institut Mittag-Leffler 2009 Abstract We study bounded ancient solutions of the Navier–Stokes equations. These are solutions with bounded velocity defined in Rn × (−1, 0). In two space dimensions we prove that such solutions are either constant or of the form u(x, t) = b(t), depending on the exact definition of admissible solutions. The general 3-dimensional problem seems to be out of reach of existing techniques, but partial results can be obtained in the case of axisymmetric solutions. We apply these results to some scenarios of potential singularity formation for axi-symmetric solutions, and obtain extensions of results in a recent paper by Chen, Strain, Tsai and Yau [4]. Weak Solution (dpeaa)DE-He213 Cauchy Problem (dpeaa)DE-He213 Stokes Equation (dpeaa)DE-He213 Mild Solution (dpeaa)DE-He213 Harnack Inequality (dpeaa)DE-He213 Nadirashvili, Nikolai aut Seregin, Gregory A. aut Šverák, Vladimir aut Enthalten in Acta mathematica Somerville, Mass. : International Press, 1882 203(2009), 1 vom: Sept., Seite 83-105 (DE-627)364462922 (DE-600)2109566-8 1871-2509 nnns volume:203 year:2009 number:1 month:09 pages:83-105 https://dx.doi.org/10.1007/s11511-009-0039-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 203 2009 1 09 83-105
language	English
source	Enthalten in Acta mathematica 203(2009), 1 vom: Sept., Seite 83-105 volume:203 year:2009 number:1 month:09 pages:83-105
sourceStr	Enthalten in Acta mathematica 203(2009), 1 vom: Sept., Seite 83-105 volume:203 year:2009 number:1 month:09 pages:83-105
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Weak Solution Cauchy Problem Stokes Equation Mild Solution Harnack Inequality
isfreeaccess_bool	false
container_title	Acta mathematica
authorswithroles_txt_mv	Koch, Gabriel @@aut@@ Nadirashvili, Nikolai @@aut@@ Seregin, Gregory A. @@aut@@ Šverák, Vladimir @@aut@@
publishDateDaySort_date	2009-09-01T00:00:00Z
hierarchy_top_id	364462922
id	SPR020477570
language_de	englisch
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author	Koch, Gabriel
spellingShingle	Koch, Gabriel misc Weak Solution misc Cauchy Problem misc Stokes Equation misc Mild Solution misc Harnack Inequality Liouville theorems for the Navier–Stokes equations and applications
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topic_title	Liouville theorems for the Navier–Stokes equations and applications Weak Solution (dpeaa)DE-He213 Cauchy Problem (dpeaa)DE-He213 Stokes Equation (dpeaa)DE-He213 Mild Solution (dpeaa)DE-He213 Harnack Inequality (dpeaa)DE-He213
topic	misc Weak Solution misc Cauchy Problem misc Stokes Equation misc Mild Solution misc Harnack Inequality
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title	Liouville theorems for the Navier–Stokes equations and applications
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title_full	Liouville theorems for the Navier–Stokes equations and applications
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author_browse	Koch, Gabriel Nadirashvili, Nikolai Seregin, Gregory A. Šverák, Vladimir
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title_sort	liouville theorems for the navier–stokes equations and applications
title_auth	Liouville theorems for the Navier–Stokes equations and applications
abstract	Abstract We study bounded ancient solutions of the Navier–Stokes equations. These are solutions with bounded velocity defined in Rn × (−1, 0). In two space dimensions we prove that such solutions are either constant or of the form u(x, t) = b(t), depending on the exact definition of admissible solutions. The general 3-dimensional problem seems to be out of reach of existing techniques, but partial results can be obtained in the case of axisymmetric solutions. We apply these results to some scenarios of potential singularity formation for axi-symmetric solutions, and obtain extensions of results in a recent paper by Chen, Strain, Tsai and Yau [4]. © Institut Mittag-Leffler 2009
abstractGer	Abstract We study bounded ancient solutions of the Navier–Stokes equations. These are solutions with bounded velocity defined in Rn × (−1, 0). In two space dimensions we prove that such solutions are either constant or of the form u(x, t) = b(t), depending on the exact definition of admissible solutions. The general 3-dimensional problem seems to be out of reach of existing techniques, but partial results can be obtained in the case of axisymmetric solutions. We apply these results to some scenarios of potential singularity formation for axi-symmetric solutions, and obtain extensions of results in a recent paper by Chen, Strain, Tsai and Yau [4]. © Institut Mittag-Leffler 2009
abstract_unstemmed	Abstract We study bounded ancient solutions of the Navier–Stokes equations. These are solutions with bounded velocity defined in Rn × (−1, 0). In two space dimensions we prove that such solutions are either constant or of the form u(x, t) = b(t), depending on the exact definition of admissible solutions. The general 3-dimensional problem seems to be out of reach of existing techniques, but partial results can be obtained in the case of axisymmetric solutions. We apply these results to some scenarios of potential singularity formation for axi-symmetric solutions, and obtain extensions of results in a recent paper by Chen, Strain, Tsai and Yau [4]. © Institut Mittag-Leffler 2009
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title_short	Liouville theorems for the Navier–Stokes equations and applications
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author2	Nadirashvili, Nikolai Seregin, Gregory A. Šverák, Vladimir
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Liouville theorems for the Navier–Stokes equations and applications

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