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

2019/09/13 by Santosh Pathak, Pathak, Santosh
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1909.07315

arXiv admin note: substantial text overlap with arXiv:1907.03099

arxiv created 2019/09/13 · arxiv updated 2019/09/17

Abstract

In this paper, we consider the Cauchy problem for the incompressible Navier-Stokes equations in ℝⁿ for n≥ 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.

Citations

• L^∞-Estimates of the Solution of the Navier-Stokes Equations for a Nondecaying Initial Data

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