Global existence of solutions to the incompressible Navier-Stokes-Vlasov equations in a time-dependent domain

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

1 LJLL - Laboratoire Jacques-Louis Lions
2 REO - Numerical simulation of biological flows

In this article, we prove the existence of global weak solutions for the in-compressible Navier-Stokes-Vlasov system in a three-dimensional time-dependent domain with absorption boundary conditions for the kinetic part. This model arises from the study of respiratory aerosol in the human airways. The proof is based on a regularization and approximation strategy designed for our time-dependent framework.

Domaines: Equations aux dérivées partielles [math.AP]

Laurent Boudin, Céline Grandmont, Ayman Moussa. Global existence of solutions to the incompressible Navier-Stokes-Vlasov equations in a time-dependent domain. Journal of Differential Equations, 2017, 262 (3), pp.1317-1340. ⟨10.1016/j.jde.2016.10.012⟩. ⟨hal-01312262⟩