LAUSR

Abstract In this paper, we study the incompressible inhomogeneous Navier-Stokes equations in bounded domains of R 3 involving bounded density functions ρ = 1 + a . Based on the corresponding theory of Besov spaces on domains, we first obtain the global existence of weak solutions ( ρ , u ) with initial data a 0 ∈ L ∞ ( Ω ) , u 0 ∈ B q , s − 1 + 3 / q ( Ω ) for 1 q 3 , 1 s ∞ . 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 .