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

Myeongju Chae, Kyungkeun Kang, Jihoon Lee

Research output: Contribution to journalArticle

17 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 languageEnglish
Pages (from-to)2431-2465
Number of pages35
JournalJournal of Differential Equations
Volume251
Issue number9
DOIs
Publication statusPublished - 2011 Nov 1

Fingerprint

Fokker Planck equation
Vlasov Equation
Existence of Weak Solutions
Fokker-Planck Equation
Classical Solution
Navier-Stokes
Global Existence
Navier Stokes equations
Drag
Three-dimension
Two Dimensions
Global Smooth Solution
Stokes System
Global Weak Solutions
Drag Force
Existence and Uniqueness Results
Incompressible Navier-Stokes Equations
Strong Solution

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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Global existence of weak and classical solutions for the Navier-Stokes-Vlasov-Fokker-Planck equations. / Chae, Myeongju; Kang, Kyungkeun; Lee, Jihoon.

In: Journal of Differential Equations, Vol. 251, No. 9, 01.11.2011, p. 2431-2465.

Research output: Contribution to journalArticle

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