A Blow-Up Criterion for 3D Compressible Isentropic Magnetohydrodynamic Equations with Vacuum
In this paper, we investigate a blow-up criterion for compressible magnetohydrodynamic equations. It is shown that if density and velocity satisfy <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<...
Ausführliche Beschreibung
Autor*in: |
Shujuan Wang [verfasserIn] Jialin Ren [verfasserIn] Rijian Su [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2024 |
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Schlagwörter: |
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Übergeordnetes Werk: |
In: Mathematics - MDPI AG, 2013, 12(2024), 5, p 687 |
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Übergeordnetes Werk: |
volume:12 ; year:2024 ; number:5, p 687 |
Links: |
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DOI / URN: |
10.3390/math12050687 |
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Katalog-ID: |
DOAJ091248566 |
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10.3390/math12050687 doi (DE-627)DOAJ091248566 (DE-599)DOAJ3ae79e4c36dd45cba1b1845c74983cef DE-627 ger DE-627 rakwb eng QA1-939 Shujuan Wang verfasserin aut A Blow-Up Criterion for 3D Compressible Isentropic Magnetohydrodynamic Equations with Vacuum 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we investigate a blow-up criterion for compressible magnetohydrodynamic equations. It is shown that if density and velocity satisfy <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mo<∥</mo<<mi<ρ</mi<<msub<<mo<∥</mo<<mrow<<msup<<mi<L</mi<<mo<∞</mo<</msup<<mrow<<mo<(</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<;</mo<<msup<<mi<L</mi<<mo<∞</mo<</msup<<mo<)</mo<</mrow<</mrow<</msub<<mo<+</mo<<mo<∥</mo<<mi mathvariant="bold"<u</mi<<msub<<mo<∥</mo<<mrow<<mi<C</mi<<mo<(</mo<<mrow<<mo<[</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<]</mo<</mrow<<mo<;</mo<<msup<<mi<L</mi<<mn<3</mn<</msup<<mo<)</mo<</mrow<</msub<<mo<<</mo<<mo<∞</mo<<mo<)</mo<</mrow<</semantics<</math<</inline-formula<, then the strong solutions to isentropic magnetohydrodynamic equations can exist globally over <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<[</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<]</mo<</mrow<</semantics<</math<</inline-formula<. Notably, our analysis accommodates the presence of an initial vacuum. compressible magnetohydrodynamic equations strong solution blow up vacuum Mathematics Jialin Ren verfasserin aut Rijian Su verfasserin aut In Mathematics MDPI AG, 2013 12(2024), 5, p 687 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:12 year:2024 number:5, p 687 https://doi.org/10.3390/math12050687 kostenfrei https://doaj.org/article/3ae79e4c36dd45cba1b1845c74983cef kostenfrei https://www.mdpi.com/2227-7390/12/5/687 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 12 2024 5, p 687 |
spelling |
10.3390/math12050687 doi (DE-627)DOAJ091248566 (DE-599)DOAJ3ae79e4c36dd45cba1b1845c74983cef DE-627 ger DE-627 rakwb eng QA1-939 Shujuan Wang verfasserin aut A Blow-Up Criterion for 3D Compressible Isentropic Magnetohydrodynamic Equations with Vacuum 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we investigate a blow-up criterion for compressible magnetohydrodynamic equations. It is shown that if density and velocity satisfy <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mo<∥</mo<<mi<ρ</mi<<msub<<mo<∥</mo<<mrow<<msup<<mi<L</mi<<mo<∞</mo<</msup<<mrow<<mo<(</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<;</mo<<msup<<mi<L</mi<<mo<∞</mo<</msup<<mo<)</mo<</mrow<</mrow<</msub<<mo<+</mo<<mo<∥</mo<<mi mathvariant="bold"<u</mi<<msub<<mo<∥</mo<<mrow<<mi<C</mi<<mo<(</mo<<mrow<<mo<[</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<]</mo<</mrow<<mo<;</mo<<msup<<mi<L</mi<<mn<3</mn<</msup<<mo<)</mo<</mrow<</msub<<mo<<</mo<<mo<∞</mo<<mo<)</mo<</mrow<</semantics<</math<</inline-formula<, then the strong solutions to isentropic magnetohydrodynamic equations can exist globally over <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<[</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<]</mo<</mrow<</semantics<</math<</inline-formula<. Notably, our analysis accommodates the presence of an initial vacuum. compressible magnetohydrodynamic equations strong solution blow up vacuum Mathematics Jialin Ren verfasserin aut Rijian Su verfasserin aut In Mathematics MDPI AG, 2013 12(2024), 5, p 687 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:12 year:2024 number:5, p 687 https://doi.org/10.3390/math12050687 kostenfrei https://doaj.org/article/3ae79e4c36dd45cba1b1845c74983cef kostenfrei https://www.mdpi.com/2227-7390/12/5/687 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 12 2024 5, p 687 |
allfields_unstemmed |
10.3390/math12050687 doi (DE-627)DOAJ091248566 (DE-599)DOAJ3ae79e4c36dd45cba1b1845c74983cef DE-627 ger DE-627 rakwb eng QA1-939 Shujuan Wang verfasserin aut A Blow-Up Criterion for 3D Compressible Isentropic Magnetohydrodynamic Equations with Vacuum 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we investigate a blow-up criterion for compressible magnetohydrodynamic equations. It is shown that if density and velocity satisfy <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mo<∥</mo<<mi<ρ</mi<<msub<<mo<∥</mo<<mrow<<msup<<mi<L</mi<<mo<∞</mo<</msup<<mrow<<mo<(</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<;</mo<<msup<<mi<L</mi<<mo<∞</mo<</msup<<mo<)</mo<</mrow<</mrow<</msub<<mo<+</mo<<mo<∥</mo<<mi mathvariant="bold"<u</mi<<msub<<mo<∥</mo<<mrow<<mi<C</mi<<mo<(</mo<<mrow<<mo<[</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<]</mo<</mrow<<mo<;</mo<<msup<<mi<L</mi<<mn<3</mn<</msup<<mo<)</mo<</mrow<</msub<<mo<<</mo<<mo<∞</mo<<mo<)</mo<</mrow<</semantics<</math<</inline-formula<, then the strong solutions to isentropic magnetohydrodynamic equations can exist globally over <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<[</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<]</mo<</mrow<</semantics<</math<</inline-formula<. Notably, our analysis accommodates the presence of an initial vacuum. compressible magnetohydrodynamic equations strong solution blow up vacuum Mathematics Jialin Ren verfasserin aut Rijian Su verfasserin aut In Mathematics MDPI AG, 2013 12(2024), 5, p 687 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:12 year:2024 number:5, p 687 https://doi.org/10.3390/math12050687 kostenfrei https://doaj.org/article/3ae79e4c36dd45cba1b1845c74983cef kostenfrei https://www.mdpi.com/2227-7390/12/5/687 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 12 2024 5, p 687 |
allfieldsGer |
10.3390/math12050687 doi (DE-627)DOAJ091248566 (DE-599)DOAJ3ae79e4c36dd45cba1b1845c74983cef DE-627 ger DE-627 rakwb eng QA1-939 Shujuan Wang verfasserin aut A Blow-Up Criterion for 3D Compressible Isentropic Magnetohydrodynamic Equations with Vacuum 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we investigate a blow-up criterion for compressible magnetohydrodynamic equations. It is shown that if density and velocity satisfy <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mo<∥</mo<<mi<ρ</mi<<msub<<mo<∥</mo<<mrow<<msup<<mi<L</mi<<mo<∞</mo<</msup<<mrow<<mo<(</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<;</mo<<msup<<mi<L</mi<<mo<∞</mo<</msup<<mo<)</mo<</mrow<</mrow<</msub<<mo<+</mo<<mo<∥</mo<<mi mathvariant="bold"<u</mi<<msub<<mo<∥</mo<<mrow<<mi<C</mi<<mo<(</mo<<mrow<<mo<[</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<]</mo<</mrow<<mo<;</mo<<msup<<mi<L</mi<<mn<3</mn<</msup<<mo<)</mo<</mrow<</msub<<mo<<</mo<<mo<∞</mo<<mo<)</mo<</mrow<</semantics<</math<</inline-formula<, then the strong solutions to isentropic magnetohydrodynamic equations can exist globally over <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<[</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<]</mo<</mrow<</semantics<</math<</inline-formula<. Notably, our analysis accommodates the presence of an initial vacuum. compressible magnetohydrodynamic equations strong solution blow up vacuum Mathematics Jialin Ren verfasserin aut Rijian Su verfasserin aut In Mathematics MDPI AG, 2013 12(2024), 5, p 687 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:12 year:2024 number:5, p 687 https://doi.org/10.3390/math12050687 kostenfrei https://doaj.org/article/3ae79e4c36dd45cba1b1845c74983cef kostenfrei https://www.mdpi.com/2227-7390/12/5/687 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 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_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 12 2024 5, p 687 |
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A Blow-Up Criterion for 3D Compressible Isentropic Magnetohydrodynamic Equations with Vacuum |
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In this paper, we investigate a blow-up criterion for compressible magnetohydrodynamic equations. It is shown that if density and velocity satisfy <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mo<∥</mo<<mi<ρ</mi<<msub<<mo<∥</mo<<mrow<<msup<<mi<L</mi<<mo<∞</mo<</msup<<mrow<<mo<(</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<;</mo<<msup<<mi<L</mi<<mo<∞</mo<</msup<<mo<)</mo<</mrow<</mrow<</msub<<mo<+</mo<<mo<∥</mo<<mi mathvariant="bold"<u</mi<<msub<<mo<∥</mo<<mrow<<mi<C</mi<<mo<(</mo<<mrow<<mo<[</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<]</mo<</mrow<<mo<;</mo<<msup<<mi<L</mi<<mn<3</mn<</msup<<mo<)</mo<</mrow<</msub<<mo<<</mo<<mo<∞</mo<<mo<)</mo<</mrow<</semantics<</math<</inline-formula<, then the strong solutions to isentropic magnetohydrodynamic equations can exist globally over <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<[</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<]</mo<</mrow<</semantics<</math<</inline-formula<. Notably, our analysis accommodates the presence of an initial vacuum. |
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In this paper, we investigate a blow-up criterion for compressible magnetohydrodynamic equations. It is shown that if density and velocity satisfy <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mo<∥</mo<<mi<ρ</mi<<msub<<mo<∥</mo<<mrow<<msup<<mi<L</mi<<mo<∞</mo<</msup<<mrow<<mo<(</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<;</mo<<msup<<mi<L</mi<<mo<∞</mo<</msup<<mo<)</mo<</mrow<</mrow<</msub<<mo<+</mo<<mo<∥</mo<<mi mathvariant="bold"<u</mi<<msub<<mo<∥</mo<<mrow<<mi<C</mi<<mo<(</mo<<mrow<<mo<[</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<]</mo<</mrow<<mo<;</mo<<msup<<mi<L</mi<<mn<3</mn<</msup<<mo<)</mo<</mrow<</msub<<mo<<</mo<<mo<∞</mo<<mo<)</mo<</mrow<</semantics<</math<</inline-formula<, then the strong solutions to isentropic magnetohydrodynamic equations can exist globally over <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<[</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<]</mo<</mrow<</semantics<</math<</inline-formula<. Notably, our analysis accommodates the presence of an initial vacuum. |
abstract_unstemmed |
In this paper, we investigate a blow-up criterion for compressible magnetohydrodynamic equations. It is shown that if density and velocity satisfy <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<(</mo<<mo<∥</mo<<mi<ρ</mi<<msub<<mo<∥</mo<<mrow<<msup<<mi<L</mi<<mo<∞</mo<</msup<<mrow<<mo<(</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<;</mo<<msup<<mi<L</mi<<mo<∞</mo<</msup<<mo<)</mo<</mrow<</mrow<</msub<<mo<+</mo<<mo<∥</mo<<mi mathvariant="bold"<u</mi<<msub<<mo<∥</mo<<mrow<<mi<C</mi<<mo<(</mo<<mrow<<mo<[</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<]</mo<</mrow<<mo<;</mo<<msup<<mi<L</mi<<mn<3</mn<</msup<<mo<)</mo<</mrow<</msub<<mo<<</mo<<mo<∞</mo<<mo<)</mo<</mrow<</semantics<</math<</inline-formula<, then the strong solutions to isentropic magnetohydrodynamic equations can exist globally over <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<[</mo<<mn<0</mn<<mo<,</mo<<mi<T</mi<<mo<]</mo<</mrow<</semantics<</math<</inline-formula<. Notably, our analysis accommodates the presence of an initial vacuum. |
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container_issue |
5, p 687 |
title_short |
A Blow-Up Criterion for 3D Compressible Isentropic Magnetohydrodynamic Equations with Vacuum |
url |
https://doi.org/10.3390/math12050687 https://doaj.org/article/3ae79e4c36dd45cba1b1845c74983cef https://www.mdpi.com/2227-7390/12/5/687 https://doaj.org/toc/2227-7390 |
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Jialin Ren Rijian Su |
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