Incompressible inhomogeneous fluids in bounded domains of R-3 with bounded density

摘要

In this paper, we study the incompressible inhomogeneous Navier-Stokes equations in bounded domains of R-3 involving bounded density functions rho = 1 + a. Based on the corresponding theory of Besov spaces on domains, we first obtain the global existence of weak solutions (rho, u) with initial data a(0) is an element of L-infinity(Omega), u(0) is an element of B-q, s(-1+3/q) (Omega) for 1 < q < 3, 1 < s < infinity. Furthermore, with additional regularity assumptions on the initial velocity, we also prove the uniqueness of such a solution. It is a generalization of a result established by Huang et al. (2013) [20] for the whole space R-3. (C) 2019 Elsevier Inc. All rights reserved.