ENERGY DISSIPATION FOR WEAK SOLUTIONS OF INCOMPRESSIBLE MHD EQUATIONS
In this article, we mainly study the local equation of energy for weak solutions of 3D MHD equations. We define a dissipation term D（u, B） that steins from an eventual lack of smoothness in the solution, and then obtain a local equation of energy for weak solutions of 3D MHD equations. Finally, we c...
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| Published in | Acta mathematica scientia Vol. 33; no. 3; pp. 865 - 871 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.05.2013
School of Mathematical Sciences, Huaqiao University, Fujian 362021, China School of Mathematical Sciences, Xiamen University, Fujian 361005, China%School of Mathematical Sciences, Xiamen University, Fujian 361005, China |
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| Online Access | Get full text |
| ISSN | 0252-9602 1572-9087 |
| DOI | 10.1016/S0252-9602(13)60046-6 |
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| Abstract | In this article, we mainly study the local equation of energy for weak solutions of 3D MHD equations. We define a dissipation term D（u, B） that steins from an eventual lack of smoothness in the solution, and then obtain a local equation of energy for weak solutions of 3D MHD equations. Finally, we consider the 2D case at the end of this article. |
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| AbstractList | In this article, we mainly study the local equation of energy for weak solutions of 3D MHD equations. We define a dissipation term D(u, B) that stems from an eventual lack of smoothness in the solution, and then obtain a local equation of energy for weak solutions of 3D MHD equations. Finally, we consider the 2D case at the end of this article. In this article, we mainly study the local equation of energy for weak solutions of 3D MHD equations. We define a dissipation term D（u, B） that steins from an eventual lack of smoothness in the solution, and then obtain a local equation of energy for weak solutions of 3D MHD equations. Finally, we consider the 2D case at the end of this article. |
| Author | 高真圣 谭忠 吴国春 |
| AuthorAffiliation | School of Mathematical Sciences, Huaqiao University, Fujian 362021, China School of Mathematical Sciences, Xiamen University, Fujian 361005, China |
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| Cites_doi | 10.1007/BF02099744 10.1007/s00205-010-0295-9 10.1007/s002200050067 10.1016/0167-2789(94)90117-1 10.1002/cpa.3160360506 10.1088/0951-7715/13/1/312 10.1007/BF02780991 10.1007/BF02547354 |
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| Notes | Energy dissipation; incompressible; MHD equations In this article, we mainly study the local equation of energy for weak solutions of 3D MHD equations. We define a dissipation term D（u, B） that steins from an eventual lack of smoothness in the solution, and then obtain a local equation of energy for weak solutions of 3D MHD equations. Finally, we consider the 2D case at the end of this article. 42-1227/O Zhensheng GAO Zhong TAN Guochun WU（1.School of Mathematical Sciences, Huaqiao University, Fujian 362021, China School of Mathematical Sciences, Xiamen University, Fujian 361005, China;2.School of Mathematical Sciences, Xiamen University, Fujian 361005, China） ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
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| References_xml | – volume: 184 start-page: 443 year: 1997 end-page: 455 ident: bib7 article-title: Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD publication-title: Commun Math Phys – volume: 165 start-page: 207 year: 1994 end-page: 209 ident: bib6 article-title: Onsager's conjecture on the energery conservation for solutions of Euler's equation publication-title: Commun Math Phys – volume: Vol 1 year: 1996 ident: bib11 publication-title: Mathematical topics in fluid mechanics. Incompressible Models – volume: 36 start-page: 633 year: 1983 end-page: 664 ident: bib1 article-title: Some mathematical questions related to the MHD equations publication-title: Commun Pure Appl Math – volume: 197 start-page: 203 year: 2010 end-page: 238 ident: bib9 article-title: Global existence and large-time behavior of solutions to the three-dimensional equations of compressible magnetohydrodynamic flows publication-title: Arch Ration Mech Anal – volume: 63 start-page: 193 year: 1934 end-page: 248 ident: bib3 article-title: Essai sur le momvement d'un liquide visqueux empissant léspace publication-title: Acta Math – volume: 13 start-page: 249 year: 2000 end-page: 255 ident: bib8 article-title: Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations publication-title: Nonlinearity – year: 1998 ident: bib10 publication-title: Mathematical topics in fluid mechanics. Vol 2. Compressible Models[M] – volume: 12 start-page: 1 year: 1933 end-page: 82 ident: bib2 article-title: Etude de diverses équations intégrals nonlinéaires et de quelques problèmes que pose 1′hydrodynamique publication-title: J Math Pures Appl – volume: 6 start-page: 279 year: 1949 end-page: 287 ident: bib4 article-title: Statistical hydrodynamics publication-title: Nuovo Cimento (Supplemento) – volume: 78 start-page: 222 year: 1994 end-page: 240 ident: bib5 article-title: Energy dissipation without viscosity in ideal hydrodynamics I. Fourier analysis and local energy transfer publication-title: Physica D – volume: 165 start-page: 207 year: 1994 ident: 10.1016/S0252-9602(13)60046-6_bib6 article-title: Onsager's conjecture on the energery conservation for solutions of Euler's equation publication-title: Commun Math Phys doi: 10.1007/BF02099744 – volume: 197 start-page: 203 year: 2010 ident: 10.1016/S0252-9602(13)60046-6_bib9 article-title: Global existence and large-time behavior of solutions to the three-dimensional equations of compressible magnetohydrodynamic flows publication-title: Arch Ration Mech Anal doi: 10.1007/s00205-010-0295-9 – volume: 184 start-page: 443 year: 1997 ident: 10.1016/S0252-9602(13)60046-6_bib7 article-title: Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD publication-title: Commun Math Phys doi: 10.1007/s002200050067 – volume: 78 start-page: 222 year: 1994 ident: 10.1016/S0252-9602(13)60046-6_bib5 article-title: Energy dissipation without viscosity in ideal hydrodynamics I. Fourier analysis and local energy transfer publication-title: Physica D doi: 10.1016/0167-2789(94)90117-1 – volume: Vol 1 year: 1996 ident: 10.1016/S0252-9602(13)60046-6_bib11 – volume: 36 start-page: 633 year: 1983 ident: 10.1016/S0252-9602(13)60046-6_bib1 article-title: Some mathematical questions related to the MHD equations publication-title: Commun Pure Appl Math doi: 10.1002/cpa.3160360506 – volume: 12 start-page: 1 year: 1933 ident: 10.1016/S0252-9602(13)60046-6_bib2 article-title: Etude de diverses équations intégrals nonlinéaires et de quelques problèmes que pose 1′hydrodynamique publication-title: J Math Pures Appl – volume: 13 start-page: 249 year: 2000 ident: 10.1016/S0252-9602(13)60046-6_bib8 article-title: Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations publication-title: Nonlinearity doi: 10.1088/0951-7715/13/1/312 – year: 1998 ident: 10.1016/S0252-9602(13)60046-6_bib10 – volume: 6 start-page: 279 year: 1949 ident: 10.1016/S0252-9602(13)60046-6_bib4 article-title: Statistical hydrodynamics publication-title: Nuovo Cimento (Supplemento) doi: 10.1007/BF02780991 – volume: 63 start-page: 193 year: 1934 ident: 10.1016/S0252-9602(13)60046-6_bib3 article-title: Essai sur le momvement d'un liquide visqueux empissant léspace publication-title: Acta Math doi: 10.1007/BF02547354 |
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| Snippet | In this article, we mainly study the local equation of energy for weak solutions of 3D MHD equations. We define a dissipation term D（u, B） that steins from an... In this article, we mainly study the local equation of energy for weak solutions of 3D MHD equations. We define a dissipation term D(u, B) that stems from an... |
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| SubjectTerms | 35Q35 Dissipation Energy dissipation incompressible Magnetohydrodynamics Mathematical analysis MHD MHD equations MHD方程 Smoothness Stems Three dimensional Two dimensional 不可压 弱解 最终解 消耗 磁流体方程 耗散项 能量方程 |
| Title | ENERGY DISSIPATION FOR WEAK SOLUTIONS OF INCOMPRESSIBLE MHD EQUATIONS |
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