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 | |
| Publication status | Published - 2016 Jul 1 |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
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Large-time behavior for the Vlasov/compressible Navier-Stokes equations. / Choi, Young Pil.
In: Journal of Mathematical Physics, Vol. 57, No. 7, 071501, 01.07.2016.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 -