Global existence of weak and classical solutions for the Navier-Stokes . . . 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
Global existence of weak and classical solutions for the Navier-Stokes . . . 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
Global existence and short long time behavior of classical solutions to . . . In this paper, we investigate a fluid-particle model defined in the whole space R 3 and the periodic domain T 3 This model consists of the incompressible inhomogeneous Navier–Stokes (NS) equations and the Vlasov–Fokker–Planck (VFP) equation which couple together via the friction force
The incompressible inhomogeneous Navier-Stokes-Vlasov-Fokker-Planck . . . In particular, we establish the optimal rates of convergence to equilibrium uniformly in Navier-Stokes Then, we construct global solutions to the inhomogeneous Euler-Fokker-Planck equations via the vanishing viscosity limit
Global weak solution to the inhomogeneous Navier–Stokes–Vlasov . . . An initial-boundary value problem is studied in a bounded domain with large initial data The existence of global weak solution is established through an approximation scheme, a fixed point argument, energy estimates, and a weak convergence method
Global weak solutions to the Vlasov–Poisson–Fokker–Planck–Navier–Stokes . . . The system describes the evolution of charged particles ensemble dispersed in an isentropic fluid For the adiabatic coefficient , we establish the global existence of weak solutions to this system with arbitrary large initial and boundary data