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Global stability of large solutions to the 3D Navier-Stokes equations

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Abstract

We prove the stability of mildly decaying global strong solutions to the Navier-Stokes equations in three space dimensions. Combined with previous results on the global existence of large solutions with various symmetries, this gives the first global existence theorem for large solutions with approximately symmetric initial data. The stability of unforced 2D flow under 3D perturbations is also obtained.

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Author notes

  1. R. Racke

    Present address: Institut für Angewandte Mathematik, Universität Bonn, Wegelerstrasse 10, D-53115, Bonn, Germany

Authors and Affiliations

  1. Department of Mathematics, University of California, 93106, Santa Barbara, CA, USA

    G. Ponce, R. Racke & T. C. Sideris

  2. Department of Mathematics, University of California, 92717, Irvine, CA, USA

    E. S. Titi

  3. Center for Applied Mathematics, Cornell University, 14853, Ithaca, NY, USA

    E. S. Titi

Authors
  1. G. Ponce
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  2. R. Racke
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  3. T. C. Sideris
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  4. E. S. Titi
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Communicated by A. Jaffe

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Ponce, G., Racke, R., Sideris, T.C. et al. Global stability of large solutions to the 3D Navier-Stokes equations. Commun.Math. Phys. 159, 329–341 (1994). https://doi.org/10.1007/BF02102642

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  • DOI: https://doi.org/10.1007/BF02102642

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