Global weak solutions to a Vlasov‐Fokker‐Planck/compressible non‐Newtonian fluid system of equations

Abstract

AbstractThis article is devoted to a coupled microscopic/macroscopic model describing the evolution of particles dispersed in a fluid. The system consists in a Vlasov‐Fokker‐Planck equation to describe the microscopic motion of the particles coupled to the equations for a compressible non‐Newtonian fluid. An initial‐boundary value problem is studied in a bounded domain with the divergence of the velocity field keeping bounded. The existence of global weak solution is established through an approximation scheme, a fixed point argument, the lower semi‐continuity of monotone operators, energy estimates and the principle of compensated compactness.