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2005, Volume 13, Issue 5: 1153-1186. Doi: 10.3934/dcds.2005.13.1153
This issue Previous Article Hausdorff dimension for non-hyperbolic repellers II: DA diffeomorphisms Next Article Another proof of the averaging principle for fully coupled dynamical systems with hyperbolic fast motions

Multiscale analysis in Lagrangian formulation for the 2-D incompressible Euler equation

  • 1.

    Department of Applied and Computational Mathematics, California Institute of Technology, Pasadena, CA 91125

  • 2.

    School of Mathematics and System Science, Shandong University, Jinan, 250100

  • 3.

    Applied and Computational Mathematics, California Institute of Technology, Pasadena, CA 91125

Received:  October 31, 2004
Revised:  February 28, 2005
Published:  September 2005
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    Abstract
  • We perform a systematic multiscale analysis for the 2-D incompressible Euler equation with rapidly oscillating initial data using a Lagrangian approach. The Lagrangian formulation enables us to capture the propagation of the multiscale solution in a natural way. By making an appropriate multiscale expansion in the vorticity-stream function formulation, we derive a well-posed homogenized equation for the Euler equation. Based on the multiscale analysis in the Lagrangian formulation, we also derive the corresponding multiscale analysis in the Eulerian formulation. Moreover, our multiscale analysis reveals some interesting structure for the Reynolds stress term, which provides a theoretical base for establishing systematic multiscale modeling of 2-D incompressible flow.
    Mathematics Subject Classification: 76F25, 76B47, 35L45.

    Citation:
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