scholarly journals Large time behavior of the solutions to the Boltzmann equation with specular reflective boundary condition

2007 ◽  
Vol 240 (2) ◽  
pp. 399-429 ◽  
Author(s):  
Feimin Huang ◽  
Yi Wang
Keyword(s):  
Boundary Condition ◽  
Boltzmann Equation ◽  
Large Time ◽  
Large Time Behavior ◽  
Time Behavior ◽  
The Boltzmann Equation

EXPONENTIAL STABILITY OF STATIONARY SOLUTIONS TO THE DISCRETE BOLTZMANN EQUATION IN A BOUNDED DOMAIN

1992 ◽  
Vol 02 (02) ◽  
pp. 239-248 ◽  
Author(s):  
SHUICHI KAWASHIMA
Keyword(s):  
Boltzmann Equation ◽  
Exponential Stability ◽  
Bounded Domain ◽  
Large Time ◽  
Stationary Solutions ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Crucial Point ◽  
Boundary Estimates ◽  
Discrete Boltzmann Equation

Large-time behavior of solutions of the discrete Boltzmann equation in a bounded domain is studied. The boundary conditions considered are pure diffuse relection and general reflection. Under suitable assumptions it is proved that a unique solution exists globally in time and converges to the corresponding unique stationary solution exponentially as time goes to infinity. The crucial point of the proof is in the derivation of desired boundary estimates of the solution subordinate to the general reflection.

scholarly journals Large time behavior of solutions to the compressible Navier–Stokes equations in an infinite layer under slip boundary condition

2016 ◽  
Vol 26 (14) ◽  
pp. 2617-2649 ◽  
Author(s):  
Abulizi Aihaiti ◽  
Shota Enomoto ◽  
Yoshiyuki Kagei
Keyword(s):  
Boundary Condition ◽  
Large Time ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Large Time Behavior ◽  
Navier Stokes ◽  
Time Behavior ◽  
Navier Stokes Equations ◽  
Infinite Layer ◽  
Slip Boundary

This paper is concerned with large time behavior of solutions to the compressible Navier–Stokes equations in an infinite layer of [Formula: see text] under slip boundary condition. It is shown that if the initial data is sufficiently small, the global solution uniquely exists and the large time behavior of the solution is described by a superposition of one-dimensional diffusion waves.

scholarly journals Large Time Behavior of the Vlasov-Poisson-Boltzmann System

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Li Li ◽  
Shuilin Jin ◽  
Li Yang
Keyword(s):  
Boltzmann Equation ◽  
Large Time ◽  
Charged Particles ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Time Stability ◽  
Poisson Boltzmann

The motion of dilute charged particles can be modeled by Vlasov-Poisson-Boltzmann system. We study the large time stability of the VPB system. To be precise, we prove that when time goes to infinity, the solution of VPB system tends to global Maxwellian state in a rateOt−∞, by using a method developed for Boltzmann equation without force in the work of Desvillettes and Villani (2005). The improvement of the present paper is the removal of condition on parameterλas in the work of Li (2008).

GLOBAL SOLUTIONS TO THE BOLTZMANN EQUATION WITH EXTERNAL FORCES

2005 ◽  
Vol 03 (02) ◽  
pp. 157-193 ◽  
Author(s):  
SEIJI UKAI ◽  
TONG YANG ◽  
HUIJIANG ZHAO
Keyword(s):  
Boltzmann Equation ◽  
Type System ◽  
Global Solutions ◽  
Stationary Solutions ◽  
Large Time Behavior ◽  
Classical Solutions ◽  
Time Behavior ◽  
Potential Force ◽  
Global Classical Solutions ◽  
The Boltzmann Equation

For the Boltzmann equation with an external potential force depending only on the space variables, there is a family of stationary solutions, which are local Maxwellians with space dependent density, zero velocity and constant temperature. In this paper, we will study the nonlinear stability of these stationary solutions by using the energy method. The analysis combines the analytic techniques used for the conservation laws using the fluid-type system derived from the Boltzmann equation (cf. [14]) and the dissipative effects on the fluid and non-fluid components of the Boltzmann equation through the celebrated H-theorem. To our knowledge, this is the first result on the global classical solutions to the Boltzmann equation with external force and non-trivial large time behavior in the whole space.

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