Asymptotic analysis for a Vlasov-Fokker-Planck/Navier-Stokes system in a bounded domain

Young Pil Choi, Jinwook Jung

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)2213-2295
Number of pages83
JournalMathematical Models and Methods in Applied Sciences
Volume31
Issue number11
DOIs
Publication statusPublished - 2021 Oct 1

Bibliographical note

Publisher Copyright:
© 2021 World Scientific Publishing Company.

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Asymptotic analysis for a Vlasov-Fokker-Planck/Navier-Stokes system in a bounded domain'. Together they form a unique fingerprint.

Cite this