A priori estimates in terms of the maximum norm for the solution of the Navier-Stokes equations for the periodic initial data

Santosh Pathak

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arXiv · 1909.07315

A priori estimates in terms of the maximum norm for the solution of the Navier-Stokes equations for the periodic initial data

Santosh Pathak

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Abstract

In this paper, we consider the Cauchy problem for the incompressible Navier-Stokes equations in $\mathbb{R}^n$ for $n\geq 3 $ with smooth periodic initial data and derive a priori estimtes of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial data. This paper is a special case of a paper by H-O Kreiss and J. Lorenz which also generalizes the main result of their paper to higher dimension.

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Santosh Pathak. 2019-09-13. A priori estimates in terms of the maximum norm for the solution of the Navier-Stokes equations for the periodic initial data. https://arxiv.org/abs/1909.07315

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