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Doubly Connected V-States for the Generalized Surface Quasi-Geostrophic Equations

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Abstract

In this paper, we prove the existence of doubly connected V-states for the generalized SQG equations with α ∈]0, 1[. They can be described by countable branches bifurcating from the annulus at some explicit “eigenvalues” related to Bessel functions of the first kind. Contrary to Euler equations Hmidi et al. (Doubly connected V-states for the planar Euler equations, arXiv:1409.7096, 2015), we find V-states rotating with positive and negative angular velocities. At the end of the paper we discuss some numerical experiments concerning the limiting V-states.

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics and Operations Research, Faculty of Science and Technology, University of the Basque Country UPV/EHU, Barrio Sarriena S/N, 48940, Leioa, Spain

    Francisco de la Hoz

  2. IRMAR, Université de Rennes 1, Campus de Beaulieu, 35 042, Rennes Cedex, France

    Zineb Hassainia & Taoufik Hmidi

Authors
  1. Francisco de la Hoz
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  2. Zineb Hassainia
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  3. Taoufik Hmidi
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Correspondence to Taoufik Hmidi.

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Communicated by L. Saint-Raymond

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de la Hoz, F., Hassainia, Z. & Hmidi, T. Doubly Connected V-States for the Generalized Surface Quasi-Geostrophic Equations. Arch Rational Mech Anal 220, 1209–1281 (2016). https://doi.org/10.1007/s00205-015-0953-z

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