American Institute of Mathematical Sciences

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January  2000, 6(1): 191-210. doi: 10.3934/dcds.2000.6.191

Renormalization group method: Application to Navier-Stokes equation

I. Moise 1, and  Roger Temam 2,

1. 

The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, Indiana 47405, United States
2. 

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

Received  October 1999 Published  December 1999

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, Galerkin method., Navier­Stokes equations.
Mathematics Subject Classification: 35Q10, 35Q30, 76D05, 35B20. .
Citation: I. Moise, Roger Temam. Renormalization group method: Application to Navier-Stokes equation. Discrete & Continuous Dynamical Systems, 2000, 6 (1) : 191-210. doi: 10.3934/dcds.2000.6.191
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