Hydrodynamic limit for the inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck equations
The authors study the hydrodynamic limit for the inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck (NS/VFP) equations in 2D or 3D bounded domains when the initial density is bounded away from zero. By employing the relative entropy techniques, the authors can first establish the strong convergence of the macroscopic density of particles in \(L^\infty (0, T; L^1(\Omega))\), and then they prove that weak solutions of the NS/VFP equations converge to the smooth solution of the limiting incompressible fluid model. Moreover, taking advantage of a compactness result for Orlicz spaces in 2D, the authors also obtain the hydrodynamic limit in the 2D case even when there is initial vacuum. The result of this paper extends the works of \textit{T. Goudon} et al. [Indiana Univ. Math. J. 53, No. 6, 1495--1515 (2004; Zbl 1085.35117)] and \textit{A. Mellet} and \textit{A. Vasseur} [Commun. Math. Phys. 281, No. 3, 573--596 (2008; Zbl 1155.35415)] to the inhomogeneous fluid case.
inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck equations
scientific article; zbMATH DE number 7191470
scientific article