Global well-posedness is proven for the 3D inhomogeneous Navier-Stokes system with discontinuous density and small velocity in critical Besov spaces, yielding the first forward self-similar solutions.
Abidi, ´Equation de Navier-Stokes avec densit´ e et viscosit´ e vari ables dans l’espace critique
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Global well-posedness and self-similar solution of the inhomogeneous Navier-Stokes system
Global well-posedness is proven for the 3D inhomogeneous Navier-Stokes system with discontinuous density and small velocity in critical Besov spaces, yielding the first forward self-similar solutions.