Global weak solutions for a Vlasov–Fokker–Planck/Navier–Stokes system with nonhomogeneous boundary data

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Yue Li
Keyword(s):  
Weak Solutions ◽  
Boundary Data ◽  
Stokes System ◽  
Navier Stokes ◽  
Global Weak Solutions ◽  
Nonhomogeneous Boundary ◽  
Nonhomogeneous Boundary Data ◽  
Fokker Planck

GLOBAL WEAK SOLUTIONS FOR A VLASOV–FOKKER–PLANCK/NAVIER–STOKES SYSTEM OF EQUATIONS

2007 ◽  
Vol 17 (07) ◽  
pp. 1039-1063 ◽  
Author(s):  
A. MELLET ◽  
A. VASSEUR
Keyword(s):  
Weak Solutions ◽  
Stokes System ◽  
Fluid Velocity ◽  
Planck Equation ◽  
Coupled System ◽  
Navier Stokes ◽  
Global Weak Solutions ◽  
Navier Stokes Equation ◽  
Reflection Boundary ◽  
Fokker Planck

We establish the existence of a weak solutions for a coupled system of kinetic and fluid equations. More precisely, we consider a Vlasov–Fokker–Planck equation coupled to compressible Navier–Stokes equation via a drag force. The fluid is assumed to be barotropic with γ-pressure law (γ > 3/2). The existence of weak solutions is proved in a bounded domain of ℝ3 with homogeneous Dirichlet conditions on the fluid velocity field and Dirichlet or reflection boundary conditions on the kinetic distribution function.

Global weak solutions of the Navier–Stokes–Fokker–Planck system

2013 ◽  
Vol 65 (2) ◽  
pp. 212-248 ◽  
Author(s):  
S. M. Egorov ◽  
E. Ya. Khruslov
Keyword(s):  
Weak Solutions ◽  
Navier Stokes ◽  
Global Weak Solutions ◽  
Fokker Planck
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