Resumen de Global well-posedness of 3-D inhomogeneous Navier–Stokes system with ill-prepared initial data

Ping Zhang, Zhifei Zhang

• In this paper, we investigate the global well-posedness of 3-D incompressible inhomogeneous Navier–Stokes system with ill-prepared initial data of the form (1+ϵβa0(xh,ϵx3),(ϵ1−αvh0,ϵ−αv30)(xh,ϵx3)) for any α∈]0,1/3[,β>2α, and ϵ being sufficiently small. This result improves the global well-posedness result for so-called well-prepared initial data, which corresponds to the case of α=0.