The Asymptotic Analysis of the Complete Fluid System on a Varying Domain: From the Compressible to the Incompressible Flow

2017 ◽  
Vol 49 (5) ◽  
pp. 3299-3334
Author(s):  
Aneta Wróblewska-Kamińska
Keyword(s):  
Asymptotic Analysis ◽  
Incompressible Flow ◽  
Fluid System

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.

Three-dimensional asymptotic analysis of multiple-electroded piezoelectric laminates

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 317-324 ◽  
Author(s):  
Zhen-Qiang Cheng ◽  
R. C. Batra
Keyword(s):  
Asymptotic Analysis ◽  
Three Dimensional
Sign in / Sign up

Export Citation Format

Share Document