Energy equality and uniqueness of weak solutions to MHD equations in L∞(0,T;Ln(Ω))

In this paper, we study the energy equality and the uniqueness of weak solutions to the MHD equations in the critical space L ∞ (0, T ; L n (Ω)). We prove that if the velocity u belongs to the critical space L ∞ (0, T ; L n (Ω)), the energy equality holds. On the basis of the energy equality, we fur...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 25; no. 5; pp. 803 - 814
Main Authors Yong, Yan, Jiu, Quan Sen
Format Journal Article
LanguageEnglish
Published Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.05.2009
Springer Nature B.V
Subjects
Energy
Equality
Mathematical analysis
Mathematics
Mathematics and Statistics
Navier-Stokes equations
Studies
Velocity
MHD equations
uniqueness
35Q35
76B03
energy equality
35Q99
weak solutions
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Summary:In this paper, we study the energy equality and the uniqueness of weak solutions to the MHD equations in the critical space L ∞ (0, T ; L n (Ω)). We prove that if the velocity u belongs to the critical space L ∞ (0, T ; L n (Ω)), the energy equality holds. On the basis of the energy equality, we further prove that the weak solution to the MHD equations is unique.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-009-7214-8