Global Existence and Large Time Behavior of Strong Solutions for 3D Nonhomogeneous Heat-Conducting Magnetohydrodynamic Equations

2021 ◽  
Author(s):  
Xin Zhong
Keyword(s):  
Global Existence ◽  
Large Time ◽  
Strong Solutions ◽  
Large Time Behavior ◽  
Heat Conducting ◽  
Time Behavior ◽  
Magnetohydrodynamic Equations ◽  
Nonhomogeneous Heat

scholarly journals The global Cauchy problem for compressible Euler equations with a nonlocal dissipation

2019 ◽  
Vol 29 (01) ◽  
pp. 185-207 ◽  
Author(s):  
Young-Pil Choi
Keyword(s):  
Global Existence ◽  
Euler Equations ◽  
Large Time ◽  
Strong Solutions ◽  
Large Time Behavior ◽  
Local Alignment ◽  
Time Behavior ◽  
Unique Strong Solution ◽  
Global Existence And Uniqueness ◽  
Isothermal Euler Equations

This paper studies the global existence and uniqueness of strong solutions and its large-time behavior for the compressible isothermal Euler equations with a nonlocal dissipation. The system is rigorously derived from the kinetic Cucker–Smale flocking equation with strong local alignment forces and diffusions through the hydrodynamic limit based on the relative entropy argument. In a perturbation framework, we establish the global existence of a unique strong solution for the system under suitable smallness and regularity assumptions on the initial data. We also provide the large-time behavior of solutions showing the fluid density and the velocity converge to its averages exponentially fast as time goes to infinity.

Global existence and large time behavior of strong solutions to the nonhomogeneous heat conducting magnetohydrodynamic equations with large initial data and vacuum

2021 ◽  
pp. 1-27
Author(s):  
Xin Zhong
Keyword(s):  
Initial Data ◽  
Large Time ◽  
Initial Density ◽  
Decay Rates ◽  
Energy Estimates ◽  
Heat Conducting ◽  
Time Behavior ◽  
Two Dimensional ◽  
Magnetohydrodynamic Equations ◽  
Nonhomogeneous Heat

We investigate an initial boundary value problem of two-dimensional nonhomogeneous heat conducting magnetohydrodynamic equations. We prove that there exists a unique global strong solution. Moreover, we also obtain the large time decay rates of the solution. Note that the initial data can be arbitrarily large and the initial density allows vacuum states. Our method relies upon the delicate energy estimates and Desjardins’ interpolation inequality (B. Desjardins, Regularity results for two-dimensional flows of multiphase viscous fluids, Arch. Rational Mech. Anal. 137(2) (1997) 135–158).

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