Global Strong Solutions to Magnetohydrodynamics with Density-Dependent Viscosity and Degenerate Heat-Conductivity

Abstract

We deal with the equations of a planar magnetohydrodynamic compressible flow with the viscosity depending on the specific volume of the gas and the heat conductivity proportional to a positive power of the temperature. Under the same conditions on the initial data as those of the constant viscosity and heat conductivity case ([Kazhikhov (1987)], we obtain the global existence and uniqueness of strong solutions which means no shock wave, vacuum, or mass or heat concentration will be developed in finite time, although the motion of the flow has large oscillations and the interaction between the hydrodynamic and magnetodynamic effects is complex. Our result can be regarded as a natural generalization of the Kazhikhov's theory for the constant viscosity and heat conductivity case to that of nonlinear viscosity and degenerate heat-conductivity.

arXiv comment16. arXiv admin note: text overlap with arXiv:1809.02498

References in corpus (3)

• Global strong solutions to the planar compressible magnetohydrodynamic equations with large initial data and vaccum
• On the Rayleigh-Taylor instability for incompressible viscous magnetohydrodynamic equations
• Nonlinearly Exponential Stability of Compressible Navier-Stokes System with Degenerate Heat-Conductivity

Cited by in corpus (3)

• On the Global Strong Solutions to Magnetohydrodynamics with Density-Dependent Viscosity and Degenerate Heat-Conductivity in Unbounded Domains
• Global existence of strong solutions to the planar compressible magnetohydrodynamic equations with large initial data in unbounded domains
• Large-time Behavior of Magnetohydrodynamics with Temperature-Dependent Heat-Conductivity