Large-time behavior for the Vlasov/compressible Navier-Stokes equations

Young Pil Choi

doi:10.1063/1.4955026

Large-time behavior for the Vlasov/compressible Navier-Stokes equations

Young Pil Choi

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We establish the large-time behavior for the coupled kinetic-fluid equations. More precisely, we consider the Vlasov equation coupled to the compressible isentropic Navier-Stokes equations through a drag forcing term. For this system, the large-time behavior shows the exponential alignment between particles and fluid velocities as time evolves. This improves the previous result by Bae et al. [Discrete Contin. Dyn. Syst. 34, 4419-4458 (2014)] in which they considered the Vlasov/Navier-Stokes equations with nonlocal velocity alignment forces for particles. Employing a new Lyapunov functional measuring the fluctuations of momentum and mass from the averaged quantities, we refine assumptions for the large-time behavior of the solutions to that system.

Original language	English
Article number	071501
Journal	Journal of Mathematical Physics
Volume	57
Issue number	7
DOIs	https://doi.org/10.1063/1.4955026
Publication status	Published - 2016 Jul 1

Bibliographical note

Funding Information:
The author warmly thanks the anonymous referee for helpful comments. The author was supported by Engineering and Physical Sciences Research Council (Grant No. EP/K008404/1) and the ERC-Starting Grant HDSPCONTR "High-Dimensional Sparse Optimal Control." The work is supported by the Alexander von Humboldt Foundation through the Humboldt Research Fellowship for Postdoctoral Researchers.

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "We establish the large-time behavior for the coupled kinetic-fluid equations. More precisely, we consider the Vlasov equation coupled to the compressible isentropic Navier-Stokes equations through a drag forcing term. For this system, the large-time behavior shows the exponential alignment between particles and fluid velocities as time evolves. This improves the previous result by Bae et al. [Discrete Contin. Dyn. Syst. 34, 4419-4458 (2014)] in which they considered the Vlasov/Navier-Stokes equations with nonlocal velocity alignment forces for particles. Employing a new Lyapunov functional measuring the fluctuations of momentum and mass from the averaged quantities, we refine assumptions for the large-time behavior of the solutions to that system.",

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