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.
Density-dependent incompressible Navier--Stokes equations in critical tent spaces
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In this article, we prove the existence of global solutions to the inhomogeneous incompressible Navier--Stokes equations, whenever the initial velocity belongs to a certain subspace of $\mathrm{BMO}^{-1}$, and the initial density is sufficiently close to $1$ in the uniform metric. This is a natural extension to the variable density case of the celebrated result by H. Koch and D. Tataru concerning the classical Navier-Stokes equations.
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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.