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arXiv · 1301.7155

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

Walter Craig·Xiangdi Huang·Yun Wang
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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 $\dot{H}^{\frac12}$-norm, which also satisfies a natural compatibility condition. A key point of the theorem is that the initial density need not be strictly positive.

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Walter Craig, Xiangdi Huang, Yun Wang. 2013-01-30. Global Wellposeness for the 3D inhomogeneous incompressible Navier-Stokes equations. https://doi.org/10.1007/s00021-013-0133-6

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