Between homogeneous and inhomogeneous Navier-Stokes systems: the issue of stability

Abstract

We construct large velocity vector solutions to the three dimensional inhomogeneous Navier-Stokes system. The result is proved via the stability of two dimensional solutions with constant density, under the assumption that initial density is point-wisely close to a constant. Key elements of our approach are estimates in the maximal regularity regime and the Lagrangian coordinates. Considerations are done in the whole ${\mathbb{R}}^3$.

38 pages, the decay estimates of 2D Navier-Stokes system are improved. JDE to appear