On convergence to equilibria of flows of compressible viscous fluids under in/out–flux boundary conditions
Entropy conjugacy for Markov multi-maps of the interval
Steady asymmetric vortex pairs for Euler equations
Zineb Hassainia 1, and Taoufik Hmidi 2,
NYU, Abu Dhabi, Saadiyat Marina District, P.O. Box 129188, Abu Dhabi, UAE
IRMAR, Université de Rennes 1, Campus de Beaulieu, 35 042 Rennes cedex, France
In this paper, we study the existence of co-rotating and counter-rotating unequal-sized pairs of simply connected patches for Euler equations. In particular, we prove the existence of curves of steadily co-rotating and counter-rotating asymmetric vortex pairs passing through a point vortex pairs with unequal circulations. We also provide a careful study of the asymptotic behavior for the angular velocity and the translating speed close to the point vortex pairs.
Keywords: Euler equations, vortex dynamics, steady vortex pairs, desingularization, implicit function theorem.
Mathematics Subject Classification: Primary: 35Q35, 35Q31; Secondary: 53C35, 76C05.
Citation: Zineb Hassainia, Taoufik Hmidi. Steady asymmetric vortex pairs for Euler equations. Discrete & Continuous Dynamical Systems - A, doi: 10.3934/dcds.2020348
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Zineb Hassainia Taoufik Hmidi