Renormalization group method: Application to Navier-Stokes equation

I. Moise; Roger Temam

doi:10.3934/dcds.2000.6.191

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2000, Volume 6, Issue 1: 191-210. Doi: 10.3934/dcds.2000.6.191

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Renormalization group method: Application to Navier-Stokes equation

I. Moise¹ and
Roger Temam^2,

1.
The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, Indiana 47405
2.
The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 E. 3rd St., Rawles Hall, Bloomington, IN 47405

Received: September 30, 1999

Published: December 1999

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Abstract

The aim of this article is to present a rather unusual and partly heuristic application of the renormalization group (RG) theory to the Navier-Stokes equations with space periodic boundary conditions. We obtain in this way a new nonlinear renormalized equation with a nonlinear term which is invariant under the Stokes operator. Its relation to the Navier-Stokes equations is investigated for non-resonant domains.

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Mathematics Subject Classification: 35Q10, 35Q30, 76D05, 35B20.

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