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Journal of Statistical Physics

, Volume 135, Issue 4, pp 737–750 | Cite as

A New Boundary Problem for the Two Dimensional Navier-Stokes System

  • Efim Dinaburg
  • Dong Li
  • Yakov G. Sinai
Article

Abstract

We formulate a new boundary value problem for the 2D Navier-Stokes system on the unit square. Under some suitable assumptions on the initial velocity, we obtain quantitative decay estimates of the Fourier modes of both the vorticity and the velocity. It is found that in one direction the Fourier modes decay exponentially and along the other direction their decay is only power like.

Keywords

Navier-Stokes equations 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Institute of Physics of EarthRussia Academy of SciencesMoscowRussia
  2. 2.School of MathematicsInstitute for Advanced StudyPrincetonUSA
  3. 3.Mathematics DepartmentPrinceton UniversityPrincetonUSA

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