Global Wellposeness for the 3D inhomogeneous incompressible Navier-Stokes equations

Abstract

This paper addresses the three-dimensional Navier-Stokes equations for an incompressible fluid whose density is permitted to be inhomogeneous. We establish a theorem of global existence and uniqueness of strong solutions for initial data with small ${\dot{H}}^{\frac{1}{2}}$-norm, which also satisfies a natural compatibility condition. A key point of the theorem is that the initial density need not be strictly positive.

15 pages

References in corpus (2)

• Global Strong solution with vacuum to the 2D nonhomogeneous incompressible MHD system
• Global wellposedness to incompressible inhomogeneous fluid system with bounded density and non-Lipschitz velocity

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