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

2020/02/24 by Pedro Gabriel Fernández-Dalgo, Fernández-Dalgo, Pedro Gabriel, Oscar Jarrín +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2002.10531

openalex publication_date 2020/02/24 · openalex created_date 2022/07/24 · openalex updated_date 2026/07/28

Abstract

We consider here the magneto-hydrodynamics (MHD) equations on the whole\nspace. For the 3D case, in the setting of the weighted L² spaces we obtain a\nweak-strong uniqueness criterion provided that the velocity field and the\nmagnetic field belong to a fairly general multipliers space. On the other hand,\nwe study the local and global existence of weak suitable solutions for\nintermittent initial data, which is characterized through a local Morrey space.\nThis large initial data space was also exhibit in a contemporary work [4] in\nthe context of 3D Navier-Stokes equations. Finally, we make a discussion on the\nlocal and global existence problem in the 2D case.\n

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