### 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 |
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Article number | 071501 |

Journal | Journal of Mathematical Physics |

Volume | 57 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2016 Jul 1 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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*Journal of Mathematical Physics*, vol. 57, no. 7, 071501. https://doi.org/10.1063/1.4955026

**Large-time behavior for the Vlasov/compressible Navier-Stokes equations.** / Choi, Young Pil.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Large-time behavior for the Vlasov/compressible Navier-Stokes equations

AU - Choi, Young Pil

PY - 2016/7/1

Y1 - 2016/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84977594973&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84977594973&partnerID=8YFLogxK

U2 - 10.1063/1.4955026

DO - 10.1063/1.4955026

M3 - Article

AN - SCOPUS:84977594973

VL - 57

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 7

M1 - 071501

ER -