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
2 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, UPMC - Université Pierre et Marie Curie - Paris 6, Inria de Paris
Abstract : 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.
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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, Elsevier, 2017, ⟨10.1016/j.jde.2016.10.012⟩. ⟨hal-01312262⟩

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