Fujita-Kato Theorem for the Inhomogeneous Incompressible Navier-Stokes Equations with Nonnegative Density  

作　　者：Jianzhong Zhang Hongmei Cao 

机构地区：[1]Department of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,P.R.China

出　　处：《Communications in Mathematical Research》2023年第1期79-106,共28页数学研究通讯（英文版）

基　　金：The second author(H.Cao)is supported by the National Natural Science Foundation of China(No.12001269);the Fundamental Research Funds for the Central Universities of China.

摘　　要：.In this paper,we prove the global existence and uniqueness of so-lutions for the inhomogeneous Navier-Stokes equations with the initial data(ρ_(0),u_(0))∈L^(∞)×H^(s) _(0),s>1/2 and ||u_(0)||H^(s)_(0)≤ε0 in bounded domain Ω■R^(3),in which the density is assumed to be nonnegative.The regularity of initial data is weaker than the previous(ρ_(0),u_(0))∈(W^(1)γ∩L^(∞)×H^(1)_(0) in [13] and(ρ_(0),u_(0))∈L^(∞)×H^(1)_(0) in[7],which constitutes a positive answer to the question raised by Danchin and Mucha in[7].The methods used in this paper are mainly the classical time weighted energy estimate and Lagrangian approach,and the continuity argu-ment and shift of integrability method are applied to complete our proof.

关 键 词：Inhomogeneous Navier-Stokes equations nonnegative density global exis-tence and uniqueness 

分 类 号：O175[理学—数学]