scholarly journals Green's function and large time behavior of solutions for nonlinear evolution systems

2018 ◽  
Vol 49 (2) ◽  
pp. 249
Author(s):  
Wang Weike
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Large Time ◽  
Nonlinear Evolution ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Evolution Systems

scholarly journals GREEN'S FUNCTION AND LARGE TIME BEHAVIOR OF THE NAVIER–STOKES–MAXWELL SYSTEM

2012 ◽  
Vol 10 (02) ◽  
pp. 133-197 ◽  
Author(s):  
RENJUN DUAN
Keyword(s):  
Electromagnetic Field ◽  
Steady State ◽  
Green’S Function ◽  
Green's Function ◽  
Stokes Equations ◽  
Large Time Behavior ◽  
Navier Stokes ◽  
Constant Density ◽  
Time Behavior ◽  
Navier Stokes Equations

In this paper, we are concerned with the system of the compressible Navier–Stokes equations coupled with the Maxwell equations through the Lorentz force in three space dimensions. The asymptotic stability of the steady state with the strictly positive constant density and the vanishing velocity and electromagnetic field is established under small initial perturbations in regular Sobolev space. For that, the dissipative structure of this hyperbolic-parabolic system is studied to include the effect of the electromagnetic field into the viscous fluid and turns out to be more complicated than that in the simpler compressible Navier–Stokes system. Moreover, the detailed analysis of the Green's function to the linearized system is made with applications to derive the rate of the solution converging to the steady state.

scholarly journals Global well-posedness of the full compressible Hall-MHD equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1235-1254
Author(s):  
Qiang Tao ◽  
Canze Zhu
Keyword(s):  
Global Solution ◽  
Large Time ◽  
Initial Temperature ◽  
Large Time Behavior ◽  
Initial Energy ◽  
Mhd Equations ◽  
Well Posedness ◽  
Time Behavior ◽  
Magnetohydrodynamic Flows ◽  
Hall Mhd

Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

Large Time Behavior of Solutions to One Nonlinear Integro-Differential Equation

2008 ◽  
Vol 15 (3) ◽  
pp. 531-539
Author(s):  
Temur Jangveladze ◽  
Zurab Kiguradze
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Boundary Conditions ◽  
Large Time ◽  
Dirichlet Boundary ◽  
Large Time Behavior ◽  
Dirichlet Boundary Conditions ◽  
Time Behavior ◽  
Integro Differential Equation ◽  
Homogeneous Data

Abstract Large time behavior of solutions to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. The rate of convergence is given, too. Dirichlet boundary conditions with homogeneous data are considered.

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