2019/12/30 by Young-Pil Choi, Choi, Young-Pil, Jinwook Jung +1 · 3 citations
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1912.13134
openalex publication_date 2019/12/30 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We study an asymptotic analysis of a coupled system of kinetic and fluid\nequations. More precisely, we deal with the nonlinear Vlasov-Fokker-Planck\nequation coupled with the compressible isentropic Navier-Stokes system through\na drag force in a bounded domain with the specular reflection boundary\ncondition for the kinetic equation and homogeneous Dirichlet boundary condition\nfor the fluid system. We establish a rigorous hydrodynamic limit corresponding\nto strong noise and local alignment force. The limiting system is a type of\ntwo-phase fluid model consisting of the isothermal Euler system and the\ncompressible Navier-Stokes system. Our main strategy relies on the relative\nentropy argument based on the weak-strong uniqueness principle. For this, we\nprovide a global-in-time existence of weak solutions for the coupled\nkinetic-fluid system. We also show the existence and uniqueness of strong\nsolutions to the limiting system in a bounded domain with the kinematic\nboundary condition for the Euler system and Dirichlet boundary condition for\nthe Navier-Stokes system.\n