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Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2020

Global existence of weak solutions to the incompressible Vlasov-Navier-Stokes system coupled to convection-diffusion equations

Résumé

We study the existence of global weak solutions in a three-dimensional time-dependent bounded domain for the incompressible Vlasov-Navier-Stokes system which is coupled with two convection-diffusion equations describing the air temperature and its water vapor mass fraction. This model is presented in [6] to describe respiratory aerosols in the human airways when one takes into account the hygroscopic effects. The mathematical description of these phenomena leads us to make the assumption that the initial distribution of particles does not contain arbitrarily small particles. With this hypothesis, the proof follows [8] and is based on a reg-ularization and approximation strategy that we solve by deriving several energy estimates.
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Dates et versions

hal-02355316 , version 1 (08-11-2019)
hal-02355316 , version 2 (02-07-2020)

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Laurent Boudin, David Michel, Ayman Moussa. Global existence of weak solutions to the incompressible Vlasov-Navier-Stokes system coupled to convection-diffusion equations. Mathematical Models and Methods in Applied Sciences, 2020, 30 (8), pp.1485-1515. ⟨10.1142/S0218202520500293⟩. ⟨hal-02355316v2⟩
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