The moderately thick spray can be described by a coupled system of equations consisting of the incompressible Navier-Stokes equations and the Vlasov-Boltzmann equation. We investigate this kind of mathematical model in this paper. In particular, we study the initial value problem of the Navier-Stokes-Vlasov-Boltzmann equations. The existence of global weak solutions is established by the weak convergence method. The interesting point of our main result is to handle the model with some breakup effects while the velocity of particles is in the whole space.
Global weak solutions for SQG in bounded domains
On global weak solutions to the Cauchy problem for the Navier-Stokes equations with large $L_3$-initial data
Global Weak Solutions to a Cahn-Hilliard-Navier-Stokes System with Chemotaxis and Singular Potential
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