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 -