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arXiv · 2405.07929

On the Existence and Smoothness of the Navier-Stokes Equation I

Brian David Vasquez Campos
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Abstract

In this paper, we give a sufficient condition to guarantee the existence of a smooth solution of the Navier-Stokes Equation with the nice decreasing properties at infinity. In this way, we prove the existence of smooth physically reasonable solutions to the Navier-Stokes problem. Additionally, we show the existence of a smooth curve of entire vector fields of order 2 that extends the solution to the complex domain for positive time.

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Brian David Vasquez Campos. 2024-05-13. On the Existence and Smoothness of the Navier-Stokes Equation I. https://arxiv.org/abs/2405.07929

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