Abstract
In this paper, we consider the initial-boundary value problem of one-dimensional compressible magnetohydrodynamics flows. The existence and continuous dependence of global solutions in H1 have been established in Chen and Wang (Z Angew Math Phys 54, 608-632, 2003). We will obtain the regularity of global solutions under certain assumptions on the initial data by deriving some new a priori estimates.
Highlights
Magnetohydrodynamics (MHD) is concerned with the flow of electrically conducting fluids in the presence of magnetic fields, either externally applied or generated within the fluid by inductive action
We focus on an initial-boundary problem for the magnetohydrodynamic flows of a perfect gas with following equations of state: Rθ p=, v e = cvθ, where R is the gas constant and cv is the heat capacity of the gas at constant volume
For the radiative magnetohydrodynamic equations with self-gravitation, Ducomet and Feireisl [13] proved the existence of global-in-time solutions of this problem with arbitrarily large initial data and conservative boundary conditions on a bounded spatial domain in R3
Summary
Magnetohydrodynamics (MHD) is concerned with the flow of electrically conducting fluids in the presence of magnetic fields, either externally applied or generated within the fluid by inductive action. R satisfy the more general constitutive relations than those in [8,9], Qin [10] established the regularity and asymptotic behavior of global solutions with arbitrary initial data for a one-dimensional viscous heat-conductive real gas. For the radiative magnetohydrodynamic equations with self-gravitation, Ducomet and Feireisl [13] proved the existence of global-in-time solutions of this problem with arbitrarily large initial data and conservative boundary conditions on a bounded spatial domain in R3.
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