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

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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.

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Authors and Affiliations

  1. Institute of Physics of Earth, Russia Academy of Sciences, Bolshaya Grusinskaya, dom 10, Moscow, 123999, Russia

    Efim Dinaburg

  2. School of Mathematics, Institute for Advanced Study, 1st Einstein Drive, Princeton, NJ, 08540, USA

    Dong Li

  3. Mathematics Department, Princeton University, Princeton, NJ, 08544, USA

    Yakov G. Sinai

Authors
  1. Efim Dinaburg
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  2. Dong Li
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  3. Yakov G. Sinai
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Correspondence to Dong Li.

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Dinaburg, E., Li, D. & Sinai, Y.G. A New Boundary Problem for the Two Dimensional Navier-Stokes System. J Stat Phys 135, 737–750 (2009). https://doi.org/10.1007/s10955-009-9760-y

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  • DOI: https://doi.org/10.1007/s10955-009-9760-y

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