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Uniformly Rotating Smooth Solutions for the Incompressible 2D Euler Equations

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Abstract

In this paper, we show the existence of a family of compactly supported smooth vorticities, which are solutions of the 2D incompressible Euler equation and rotate uniformly in time and space.

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Acknowledgements

AC, DC and JGS were partially supported by the Grant MTM2014-59488-P (Spain) and ICMAT Severo Ochoa Project SEV-2015-556. AC was partially supported by the Ramón y Cajal Program RyC-2013-14317 and ERC Grant 307179-GFTIPFD. JGS was partially supported by an AMS-Simons Travel Grant. Part of this work was done while JGS was visiting ICMAT, to which he is grateful for its support. We thank Jacob Bedrossian and Vlad Vicol for helpful conversations.

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Authors and Affiliations

  1. Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, C/ Nicolas Cabrera, 13-15, 28049, Madrid, Spain

    Angel Castro & Diego Córdoba

  2. Department of Mathematics, Princeton University, 610 Fine Hall, Washington Rd, Princeton, NJ, 08544, USA

    Javier Gómez-Serrano

Authors
  1. Angel Castro
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  2. Diego Córdoba
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  3. Javier Gómez-Serrano
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Correspondence to Javier Gómez-Serrano.

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Communicated by V. Šverák

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Castro, A., Córdoba, D. & Gómez-Serrano, J. Uniformly Rotating Smooth Solutions for the Incompressible 2D Euler Equations. Arch Rational Mech Anal 231, 719–785 (2019). https://doi.org/10.1007/s00205-018-1288-3

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