Abstract:
The interactions between particles and fluid have received a bulk of attention due to a number of their applications in the field of, for example, biotechnology, medicine, and in the study of sedimentation phenomenon, compressibility of droplets of the spray, cooling tower plumes, and diesel engines, etc. In this talk, we present coupled hydrodynamic equations which can be formally derived from the Vlasov-Boltzmann/Navier-Stokes equations. More precisely, our proposed equations consist of the compressible pressureless Euler equations and the compressible isentropic Navier-Stokes equations. For the equations, we establish the global existence of classical solutions, and its large-time behavior which shows the exponential alignment between two fluid velocities. |