On formation of singularity for a fluid-particle interaction model

Abstract

We investigate the Cauchy problem of a fluid-particle interaction model with vacuum as far field density in R2, namely, compressible Navier-Stokes equations coupled with Smoluchowski equation. A blowup criterion for the strong solution of the Cauchy problem is established in terms of ‖ρ‖Lt∞Lxs, where s≥s0. This criterion extends Huang's et al. result (Acta Appl Math. 170 (2020) 185–202.) to the 2D Cauchy problem of a fluid-particle interaction model, in particular, it is independent of the velocity and the density of the particles.