Asymptotic analysis for a homogeneous bubbling regime Vlasov–Fokker–Planck/Navier–Stokes system

2020 ◽  
Vol 71 (4) ◽  
Author(s):  
Joshua Ballew
Keyword(s):  
Asymptotic Analysis ◽  
Stokes System ◽  
Navier Stokes ◽  
Fokker Planck

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.

GLOBAL WEAK SOLUTIONS FOR A VLASOV–FOKKER–PLANCK/NAVIER–STOKES SYSTEM OF EQUATIONS

2007 ◽  
Vol 17 (07) ◽  
pp. 1039-1063 ◽  
Author(s):  
A. MELLET ◽  
A. VASSEUR
Keyword(s):  
Weak Solutions ◽  
Stokes System ◽  
Fluid Velocity ◽  
Planck Equation ◽  
Coupled System ◽  
Navier Stokes ◽  
Global Weak Solutions ◽  
Navier Stokes Equation ◽  
Reflection Boundary ◽  
Fokker Planck

We establish the existence of a weak solutions for a coupled system of kinetic and fluid equations. More precisely, we consider a Vlasov–Fokker–Planck equation coupled to compressible Navier–Stokes equation via a drag force. The fluid is assumed to be barotropic with γ-pressure law (γ > 3/2). The existence of weak solutions is proved in a bounded domain of ℝ3 with homogeneous Dirichlet conditions on the fluid velocity field and Dirichlet or reflection boundary conditions on the kinetic distribution function.

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 Some preliminary observations on a defect Navier–Stokes system

2019 ◽  
Vol 347 (10) ◽  
pp. 677-684 ◽  
Author(s):  
Amit Acharya ◽  
Roger Fosdick
Keyword(s):  
Stokes System ◽  
Navier Stokes
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