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

  • Santosh Pathak University of New Mexico, Albuquerque, NM 87131, USA
Keywords: Incompressible Navier-Stokes equation, Maximum norm estimates, Periodic initial data

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.

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Author Biography

Santosh Pathak, University of New Mexico, Albuquerque, NM 87131, USA

Department of Mathematics and Statistics

Published
2019-12-31
How to Cite
Pathak, S. (2019). A priori estimates in terms of the maximum norm for the solution of the Navier-Stokes equations with periodic initial data. The Nepali Mathematical Sciences Report, 36(1-2), 39-50. https://doi.org/10.3126/nmsr.v36i1-2.29969
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Articles