The global existence and uniqueness of smooth solutions to a fluid-particle interaction model in the flowing regime

Abstract

This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime in ℝ³. Under the smallness assumption on both the external potential and the initial perturbation of the stationary solution in some Sobolev spaces, the existence and uniqueness of global smooth solutions in H³ of the system are established by using the careful energy method.