TY - JOUR

T1 - Doubly Connected V-States for the Generalized Surface Quasi-Geostrophic Equations

AU - de la Hoz, Francisco

AU - Hassainia, Zineb

AU - Hmidi, Taoufik

N1 - Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

PY - 2016/6/1

Y1 - 2016/6/1

N2 - 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.

AB - 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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U2 - 10.1007/s00205-015-0953-z

DO - 10.1007/s00205-015-0953-z

M3 - Article

AN - SCOPUS:84952889975

SN - 0003-9527

VL - 220

SP - 1209

EP - 1281

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 3

ER -