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arXiv · 2002.08270

Global-in-Time solutions of the Navier-Stokes equations

Gray Jennings
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Abstract

We establish the existence of a uniformly bounded $ C^\infty $ solution of the Navier-Stokes equations on $\mathbb{R}^3 x\ [0, \infty) $ without external forces or boundaries for a divergence free initial condition $ u_o \in \cap_m H^m $ when the viscosity $ \nu $ is $ > 0 $. Such $ C^\infty $ solution of the Navier-Stokes equations are a solution of Option A of the Millenium Prize Problem of the Clay Institute for the Navier-Stokes equations.

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Gray Jennings. 2020-02-18. Global-in-Time solutions of the Navier-Stokes equations. https://arxiv.org/abs/2002.08270

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