Existence of weak solutions to the three-dimensional density-dependent generalized incompressible magnetohydrodynamic flows

2011/12/18 by Weiping Yan, Yan, Weiping
Mathematics · #35D30 #76W05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #math.AP #math.DS #msc:35D30 #msc:76W05

paper · pdf · doi:10.48550/arxiv.1112.4121

32pages

openalex publication_date 2011/12/18 · arxiv created 2014/04/21 · arxiv updated 2014/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the equations of the unsteady viscous, incompressible, and heat conducting magnetohydrodynamic flows in a bounded three-dimensional domain with Lipschitz boundary. By an approximation scheme and a weak convergence method, the existence of a weak solution to the three-dimensional density dependent generalized incompressible magnetohydrodynamic equations with large data is obtained.

Citations

• Some mathematical questions related to the mhd equations

Related

• Global Solutions to the Three-Dimensional Full Compressible Magnetohydrodynamic Flows
• Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows
• Global weak solutions of 3D compressible magnetohydrodynamic equations subject to large external potential forces with discontinuous initial data and vacuum
• Incompressible Magnetohydrodynamic Flow with Zero Resistivity
• A blow-up criterion for strong solutions to three-dimensional compressible magnetohydrodynamic equations