ASYMPTOTIC ANALYSIS FOR A VLASOV–NAVIER–STOKES SYSTEM IN A BOUNDED DOMAIN

2010 ◽  
Vol 07 (02) ◽  
pp. 191-210
Author(s):  
NAJOUA EL GHANI
Keyword(s):  
Boundary Condition ◽  
Asymptotic Analysis ◽  
Bounded Domain ◽  
Stokes System ◽  
Fluid Velocity ◽  
Convergence Result ◽  
Limit Problem ◽  
Entropy Method ◽  
Navier Stokes ◽  
Constant Density

This article is devoted to the asymptotic analysis of a Vlasov–Navier–Stokes system in dimension two, and treat general initial data with finite mass, energy and entropy. The limit problem is the Navier–Stokes system with non-constant density. The convergence result is proved in a bounded domain of ℝ2with a homogeneous Dirichlet boundary condition on the fluid velocity field and Maxwell boundary condition on the kinetic distribution function, while the proof relies on a relative entropy method.

scholarly journals Asymptotic analysis for a Vlasov–Fokker–Planck/Navier–Stokes system in a bounded domain

2021 ◽  
pp. 1-83
Author(s):  
Young-Pil Choi ◽  
Jinwook Jung
Keyword(s):  
Boundary Condition ◽  
Asymptotic Analysis ◽  
Bounded Domain ◽  
Dirichlet Boundary Condition ◽  
Stokes System ◽  
Dirichlet Boundary ◽  
Euler System ◽  
Navier Stokes ◽  
Fluid System ◽  
Fokker Planck

We study an asymptotic analysis of a coupled system of kinetic and fluid equations. More precisely, we deal with the nonlinear Vlasov–Fokker–Planck equation coupled with the compressible isentropic Navier–Stokes system through a drag force in a bounded domain with the specular reflection boundary condition for the kinetic equation and homogeneous Dirichlet boundary condition for the fluid system. We establish a rigorous hydrodynamic limit corresponding to strong noise and local alignment force. The limiting system is a type of two-phase fluid model consisting of the isothermal Euler system and the compressible Navier–Stokes system. Our main strategy relies on the relative entropy argument based on the weak–strong uniqueness principle. For this, we provide a global-in-time existence of weak solutions for the coupled kinetic-fluid system. We also show the existence and uniqueness of strong solutions to the limiting system in a bounded domain with the kinematic boundary condition for the Euler system and Dirichlet boundary condition for the Navier–Stokes system.

scholarly journals Stationary Navier–Stokes equations with non-homogeneous boundary condition in a system of two connected layers

2012 ◽  
Vol 53 ◽  
Author(s):  
Kristina Kaulakytė
Keyword(s):  
Boundary Condition ◽  
Boundary Problem ◽  
Stokes System ◽  
Stokes Equations ◽  
Boundary Value ◽  
Homogeneous Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stationary Navier Stokes Equations

In this paper the stationary Navier–Stokes system with non-homogeneous boundary condition is studied in domain which consists of two connected layers. The extension of the boundary value, which reduces the non-homogeneous boundary problem to the homogeneous one, is constructed in this paper.

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