Global strong solutions to a compressible fluid-particle interaction model with density-dependent friction force

2025/02/27 by Fucai Li, Jinkai Ni, Li, Fucai +3 · 1 citation
#35B40 #35Q84 #76N06 #76N10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.19886

Abstract

We investigate the Cauchy problem for a fluid-particle interaction model in ℝ³. This model consists of the compressible barotropic Navier-Stokes equations and the Vlasov-Fokker-Planck equation coupled together via the density-dependent friction force. Due to the strong coupling caused by the friction force, it is a challenging problem to construct the global existence and optimal decay rates of strong solutions. In this paper, by assuming that the H²-norm of the initial data is sufficiently small, we establish the global well-posedness of strong solutions. Furthermore, if the L¹-norm of initial data is bounded, then we achieve the optimal decay rates of strong solutions and their gradients in L²-norm. The proofs rely on developing refined energy estimates and exploiting the frequency decomposition method. In addition, for the periodic domain case, our global strong solutions decay exponentially.

Cited by

• The incompressible inhomogeneous Navier-Stokes-Vlasov-Fokker-Planck equations: global well-posedness and inviscid limit

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