Global existence and vanishing viscosity limit of the compressible Navier-Stokes-Vlasov-Fokker-Planck system in critical spaces

We study multidimensional compressible fluid-particle systems at critical regularity, in which a carrier fluid and a particle phase with Fokker-Planck diffusion are coupled through a drag force. We prove the existence and uniqueness of strong solutions for the Cauchy problems of the Navier-Stokes-Vl