2016/08/29 by Yang Liu, Liu, Yang
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1608.08876
openalex publication_date 2016/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the local existence of strong solutions to the Cauchy problem of the 2D fluid-particle interaction model with vacuum as far field density. Notice that the technique used by Ding et al.\citeSBH for the corresponding 3D local well-posedness of strong solutions fails treating the 2D case, because the Lp-norm (p>2) of the velocity u cannot be controlled in terms only of √ρu and ∇ u here. In the present paper, we will use the framework of weighted approximation estimates introduced in [J. Li, Z. Liang, On classical solutions to the Cauchy problem of the two-dimensional barotropic compressible Navier-Stokes equations with vacuum, J. Math. Pures Appl. (2014) 640--671] for Navier-Stokes equations to obtain the local existence of strong solutions provided the initial density and density of particles in the mixture do not decay very slowly at infinity. In particular, the initial density can have a compact support. This paper extends Fang et al.'s result \citeDRZ and Ding et al.'s result \citeSBH, in which, the existence is obtained when the space dimension N=1 and N=3 respectively.