Global smooth solution of hydrodynamical equation for the Heisenberg paramagnet

2003 ◽  
Vol 27 (2) ◽  
pp. 181-191 ◽  
Author(s):  
Guo Boling ◽  
Han Yongqian
Keyword(s):  
Smooth Solution ◽  
Hydrodynamical Equation ◽  
Global Smooth Solution ◽  
Heisenberg Paramagnet

Global random attractor of stochastic hydrodynamical equation for the Heisenberg paramagnet with multiplicative noise on ℝd

2015 ◽  
Vol 16 (01) ◽  
pp. 1650007 ◽  
Author(s):  
Yanfeng Guo ◽  
Chunxiao Guo ◽  
Yongqian Han
Keyword(s):  
Dynamical System ◽  
Multiplicative Noise ◽  
Stochastic Equation ◽  
Random Coefficients ◽  
Random Attractor ◽  
Random Dynamical System ◽  
Hydrodynamical Equation ◽  
Priori Estimates ◽  
Heisenberg Paramagnet ◽  
Truncation Function

The stochastic hydrodynamical equation for the Heisenberg paramagnet with multiplicative noise defined on the entire [Formula: see text] is mainly investigated. The global random attractor for the random dynamical system associated with the equation is obtained. The method is to transform the stochastic equation into the corresponding partial differential equations with random coefficients by Ornstein–Uhlenbeck process. The uniform priori estimates for far-field values of solutions have been studied via a truncation function, and then the asymptotic compactness of the random dynamical system is established.

Global smooth solution for nonlinearly dampedp-system with large initial data

1999 ◽  
Vol 73 (3-4) ◽  
pp. 507-522 ◽  
Author(s):  
Changjiang ZHU ◽  
Huijiang Zhao ◽  
Xuewen XU
Keyword(s):  
Initial Data ◽  
Smooth Solution ◽  
Large Initial Data ◽  
Global Smooth Solution

Smoothing effect on the damping mechanism for an inviscid two-phase gas—liquid model

2014 ◽  
Vol 144 (2) ◽  
pp. 351-362 ◽  
Author(s):  
Lizhi Ruan
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
External Force ◽  
Smooth Solution ◽  
Smoothing Effect ◽  
Two Phase ◽  
Global Smooth Solution ◽  
Liquid Model ◽  
The Cauchy Problem

In this paper, we consider the Cauchy problem for an inviscid two-phase gas—liquid model with external force, in order to demonstrate the smoothing effect on the damping mechanism. It is shown that the Cauchy problem admits a unique global smooth solution provided that the initial data are smooth and the C0-norm of the derivative of the initial data are small.

scholarly journals Global smooth solution for a kind of two-fluid system in plasmas

2012 ◽  
Vol 252 (5) ◽  
pp. 3453-3481 ◽  
Author(s):  
Lijia Han ◽  
Jingjun Zhang ◽  
Boling Guo
Keyword(s):  
Smooth Solution ◽  
Fluid System ◽  
Global Smooth Solution ◽  
Two Fluid
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