Weak-strong uniqueness in weighted L2 spaces and weak suitable solutions in local Morrey spaces for the MHD equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:271

Article

Fernandez-Dalgo, Pedro Gabriel¹  Jarrin, Oscar² 

[1] Univ Paris Saclay, CNRS, Univ Evry, LaMME, F-91025 Evry, France

[2] Univ Tecn Ambato, Direcc Invest & Desarrollo DIDE, Ambato, Ecuador

关键词: MHD equations;    Weak-strong uniqueness;    Multipliers spaces;    Local Morrey spaces;    Global weak solutions;    Suitable solutions;   

DOI  :  10.1016/j.jde.2020.09.017

来源: Elsevier

【 摘 要 】

We consider here the magneto-hydrodynamics (MHD) equations on the whole space. For the 3D case, in the setting of the weighted L-2 spaces we obtain a weak-strong uniqueness criterion provided that the velocity field and the magnetic field belong to a fairly general multipliers space. On the other hand, we study the local and global existence of weak suitable solutions for intermittent initial data, which is characterized through a local Morrey space. This large initial data space was also exhibit in a contemporary work [4] in the context of 3D Navier-Stokes equations. Finally, we make a discussion on the local and global existence problem in the 2D case. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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