Global existence of solutions for the coupled Vlasov and Navier-Stokes equations

Laurent Boudin (1, 2) , Laurent Desvillettes (3) , Céline Grandmont (2) , Ayman Moussa (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 REO - Numerical simulation of biological flows
3 CMLA - Centre de Mathématiques et de Leurs Applications

In this work, we obtain a result of global existence for weak solutions of the three-dimensional incompressible Vlasov-Navier-Stokes equations, the coupling being done through a drag force which is linear with respect to the relative velocity of fluid and particles.

Domaines: Equations aux dérivées partielles [math.AP]

Laurent Boudin, Laurent Desvillettes, Céline Grandmont, Ayman Moussa. Global existence of solutions for the coupled Vlasov and Navier-Stokes equations. Differential and integral equations, 2009, 22 (11-12), pp.1247-1271. ⟨10.57262/die/1356019415⟩. ⟨hal-00331895⟩