具有变黏性系数的3维非齐次不可压Navier-Stokes方程解的全局适定性

On the global well-posedness of 3D inhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity

本文考虑初始速度u0∈B^(·)^(1/2)_(2,1)且具有变黏性系数的3维非齐次不可压Navier-Stokes方程小初值情形下解的全局适定性.相比Abidi和Zhang(2015)的结果,这里去掉了∥μ(ρ_(0))-1∥_(L∞)的小性假设.

In this paper,we consider the global well-posedness of 3D inhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity when the initial velocity is sufficiently small in the critical Besov space B^(·)^(1/2)_(2,1).Compared with the previous result of Abidi and Zhang(2015),our research removes the smallness assumption on the viscosityμ(ρ_(0))−1 in terms of L^(∞)-norm.