On the Cauchy problem for the nonlinear Boltzmann equation global existence uniqueness and asymptotic stability

1985 ◽  
Vol 26 (2) ◽  
pp. 334-338 ◽  
Author(s):  
N. Bellomo ◽  
G. Toscani
Keyword(s):  
Cauchy Problem ◽  
Boltzmann Equation ◽  
Asymptotic Stability ◽  
Global Existence ◽  
Nonlinear Boltzmann Equation ◽  
The Cauchy Problem

scholarly journals THE BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF IN THE WHOLE SPACE: II, GLOBAL EXISTENCE FOR HARD POTENTIAL

2011 ◽  
Vol 09 (02) ◽  
pp. 113-134 ◽  
Author(s):  
R. ALEXANDRE ◽  
Y. MORIMOTO ◽  
S. UKAI ◽  
C.-J. XU ◽  
T. YANG
Keyword(s):  
Cauchy Problem ◽  
Boltzmann Equation ◽  
Global Existence ◽  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Existence Of Solution ◽  
The Boltzmann Equation ◽  
The Cauchy Problem ◽  
Whole Space ◽  
Global Equilibrium

As a continuation of our series works on the Boltzmann equation without angular cutoff assumption, in this part, the global existence of solution to the Cauchy problem in the whole space is proved in some suitable weighted Sobolev spaces for hard potential when the solution is a small perturbation of a global equilibrium.

scholarly journals Global existence of solution for multidimensional generalized double dispersion equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiaoqiang Dai
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Dispersion Equation ◽  
Existence Of Solutions ◽  
Existence Of Solution ◽  
New Methods ◽  
Global Existence Of Solutions ◽  
The Cauchy Problem ◽  
Double Dispersion

Abstract In this paper, we study the Cauchy problem of multidimensional generalized double dispersion equation. To prove the global existence of solutions, we introduce some new methods and ideas, and fill some gaps in the established results.

scholarly journals Global existence of strong solutions for incompressible hydrodynamic flow of liquid crystals with vacuum

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1247-1257 ◽  
Author(s):  
Shijin Ding ◽  
Jinrui Huang ◽  
Fengguang Xia
Keyword(s):  
Cauchy Problem ◽  
Liquid Crystals ◽  
Global Existence ◽  
Existence And Uniqueness ◽  
Strong Solutions ◽  
Hydrodynamic Flow ◽  
Three Dimensions ◽  
Small Initial Data ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We consider the Cauchy problem for incompressible hydrodynamic flow of nematic liquid crystals in three dimensions. We prove the global existence and uniqueness of the strong solutions with nonnegative p0 and small initial data.

Sign in / Sign up

Export Citation Format

Share Document