Renormalization group method: Application to Navier-Stokes equation

Pages: 191 - 210, Volume 6, Issue 1, January 2000      doi:10.3934/dcds.2000.6.191

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I. Moise - The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, Indiana 47405, United States (email)
Roger Temam - The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 E. 3rd St., Rawles Hall, Bloomington, IN 47405, United States (email)

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.

Keywords:  Renormalization group method, Navier­Stokes equations, Galerkin method.
Mathematics Subject Classification:  35Q10, 35Q30, 76D05, 35B20.

Received: October 1999;      Available Online: December 1999.