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 R3.