Global well-posedness and large-time behavior for the inhomogeneous Vlasov-Navier-Stokes equations

Young Pil Choi, Bongsuk Kwon

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We study the global solvability and the large-time behavior of solutions to the inhomogeneous Vlasov-Navier-Stokes equations. When the initial data is sufficiently small and regular, we first show the unique existence of the global strong solution to the kinetic-fluid equations, and establish the a priori estimates for the large-time behavior using an appropriate Lyapunov functional. More specifically, we show that the velocities of particles and fluid tend to be aligned together exponentially fast, provided that the local density of the particles satisfies a certain integrability condition.

Original languageEnglish
Pages (from-to)3309-3336
Number of pages28
JournalNonlinearity
Volume28
Issue number9
DOIs
Publication statusPublished - 2015 Sep 1

Fingerprint

Vlasov Equation
Global Well-posedness
Large Time Behavior
Navier-Stokes equation
Navier Stokes equations
Navier-Stokes Equations
Global Solvability
Fluid
Fluids
fluids
Lyapunov Functional
Strong Solution
Behavior of Solutions
A Priori Estimates
Integrability
Kinetics
Tend
kinetics
estimates

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

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Global well-posedness and large-time behavior for the inhomogeneous Vlasov-Navier-Stokes equations. / Choi, Young Pil; Kwon, Bongsuk.

In: Nonlinearity, Vol. 28, No. 9, 01.09.2015, p. 3309-3336.

Research output: Contribution to journalArticle

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