Global Solutions to an initial boundary problem for the compressible 3-D MHD equations with Navier-slip and perfectly conducting boundary conditions in exterior domains

Abstract

An initial boundary value problem for compressible Magnetohydrodynamics (MHD) is considered on an exterior domain (with the first Betti number vanishes) in $R^3$ in this paper. The global existence of smooth solutions near a given constant state for compressible MHD with the boundary conditions of Navier-slip for the velocity filed and perfect conduction for the magnetic field is established. Moreover the explicit decay rate is given. In particular, the results obtained in this paper also imply the global existence of classical solutions for the full compressible Navier-Stokes equations with Navier-slip boundary conditions on exterior domains in three dimensions, which is not available in literature, to the best of knowledge of the authors'.

References in corpus (3)

• Global solutions to the three-dimensional full compressible magnetohydrodynamic flows
• Existence and Exponential Growth of Global Classical Solutions to the Compressible Navier-Stokes Equations with Slip Boundary Conditions in 3D Bounded Domains
• Global Strong Solutions to the Compressible Magnetohydrodynamic Equations with Slip Boundary Conditions in 3D Bounded Domains