Global existence of weak and classical solutions for the Navier-Stokes-Vlasov-Fokker-Planck equations

Myeongju Chae; Kyungkeun Kang; Jihoon Lee

doi:10.1016/j.jde.2011.07.016

Global existence of weak and classical solutions for the Navier-Stokes-Vlasov-Fokker-Planck equations

Myeongju Chae, Kyungkeun Kang, Jihoon Lee

Department of Mathematics

Research output: Contribution to journal › Article

20 Citations (Scopus)

Abstract

We consider a system coupling the incompressible Navier-Stokes equations to the Vlasov-Fokker-Planck equation. The coupling arises from a drag force exerted by each other. We establish existence of global weak solutions for the system in two and three dimensions. Furthermore, we obtain the existence and uniqueness result of global smooth solutions for dimension two. In case of three dimensions, we also prove that strong solutions exist globally in time for the Vlasov-Stokes system.

Original language	English
Pages (from-to)	2431-2465
Number of pages	35
Journal	Journal of Differential Equations
Volume	251
Issue number	9
DOIs	https://doi.org/10.1016/j.jde.2011.07.016
Publication status	Published - 2011 Nov 1

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All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Cite this

Chae, M., Kang, K., & Lee, J. (2011). Global existence of weak and classical solutions for the Navier-Stokes-Vlasov-Fokker-Planck equations. Journal of Differential Equations, 251(9), 2431-2465. https://doi.org/10.1016/j.jde.2011.07.016

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10.1016/j.jde.2011.07.016