scholarly journals Large-Time Behavior of Magnetohydrodynamics with Temperature-Dependent Coefficients

2021 ◽  
Author(s):  
Song Dandan
Keyword(s):  
Existence And Uniqueness ◽  
Large Time ◽  
Strong Solutions ◽  
Large Time Behavior ◽  
Growth Exponent ◽  
Time Behavior ◽  
Temperature Dependent ◽  
Magnetic Diffusivity ◽  
Positive Growth ◽  
Magnetohydrodynamic System

In this paper, we investigate the initial and boundary value problem of a planar magnetohydrodynamic system with temperature-dependent coefficients of transport, heat conductivity, and magnetic diffusivity coefficients. When all of the relative coefficients are exponentially related to the temperature, the existence and uniqueness of the global-in-time non-vacuum strong solutions are proven under some special assumptions. At the same time, the nonlinearly exponential stability of the solutions is obtained. In fact, the initial data could be large if the positive growth exponent of viscosity is small enough.

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.

Large-time behavior of strong solutions to the compressible magnetohydrodynamic system in the critical framework

2018 ◽  
Vol 15 (02) ◽  
pp. 259-290 ◽  
Author(s):  
Weixuan Shi ◽  
Jiang Xu
Keyword(s):  
Large Time ◽  
Characteristic Root ◽  
Global Solutions ◽  
Strong Solutions ◽  
Parabolic Systems ◽  
Large Time Behavior ◽  
Optimal Time ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
Mhd System

We study the compressible viscous magnetohydrodynamic (MHD) system and investigate the large-time behavior of strong solutions near constant equilibrium (away from vacuum). In the 80s, Umeda et al. considered the dissipative mechanisms for a rather general class of symmetric hyperbolic–parabolic systems, which is given by [Formula: see text] Here, [Formula: see text] denotes the characteristic root of linearized equations. From the point of view of dissipativity, Kawashima in his doctoral dissertation established the optimal time-decay estimates of [Formula: see text]-[Formula: see text]) type for solutions to the MHD system. Now, by using Fourier analysis techniques, we present more precise description for the large-time asymptotic behavior of solutions, not only in extra Lebesgue spaces but also in a full family of Besov norms with the negative regularity index. Precisely, we show that the [Formula: see text] norm (the slightly stronger [Formula: see text] norm in fact) of global solutions with the critical regularity, decays like [Formula: see text] as [Formula: see text]. Our decay results hold in case of large highly oscillating initial velocity and magnetic fields, which improve Kawashima’s classical efforts.

The large time behavior of strong solutions to a P1-approximation arising in radiating hydrodynamics

2020 ◽  
Vol 192 (2) ◽  
pp. 427-463
Author(s):  
Fuyi Xu ◽  
Meiling Chi ◽  
Gang Wang ◽  
Yonghong Wu ◽  
Yeping Li
Keyword(s):  
Large Time ◽  
Strong Solutions ◽  
Large Time Behavior ◽  
Time Behavior
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