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.
Bibliographical noteFunding Information:
The authors thank anonymous referee for his/her careful reading and valuable remarks. M. Chae’s work was supported by the National Research Foundation of Korea (NRF No. 2009-0069501). K. Kang’s work was partially supported by KRF-2008-331-C00024 and NRF No. 2009-00088692. J. Lee’s work was partially supported by the National Research Foundation of Korea (NRF No. 2009-0088692).
All Science Journal Classification (ASJC) codes
- Applied Mathematics