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 language | English |
|---|---|
| Pages (from-to) | 2431-2465 |
| Number of pages | 35 |
| Journal | Journal of Differential Equations |
| Volume | 251 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 2011 Nov 1 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
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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 journal › Article
TY - JOUR
T1 - Global existence of weak and classical solutions for the Navier-Stokes-Vlasov-Fokker-Planck equations
AU - Chae, Myeongju
AU - Kang, Kyungkeun
AU - Lee, Jihoon
PY - 2011/11/1
Y1 - 2011/11/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=79961209561&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79961209561&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2011.07.016
DO - 10.1016/j.jde.2011.07.016
M3 - Article
AN - SCOPUS:79961209561
VL - 251
SP - 2431
EP - 2465
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 9
ER -