Motivated by the statistical mechanics description of stationary 2D-turbulence, for a sinh-Poisson type equation with asymmetric nonlinearity, we construct a concentrating solution sequence in the form of a tower of singular Liouville bubbles, each of which has a different degeneracy exponent. The asymmetry parameter $γ∈(0, 1]$ corresponds to the ratio between the intensity of the negatively rotating vortices and the intensity of the positively rotating vortices. Our solutions correspond to a superposition of highly concentrated vortex configurations of alternating orientation; they extend in a nontrivial way some known results for $\gamma=1$. Thus, by analyzing the case $\gamma≠1$ we emphasize specific properties of the physically relevant parameter $\gamma$ in the vortex concentration phenomena.

Sign-changing tower of bubbles for a sinh-poisson equation with asymmetric exponents / Pistoia, Angela; Ricciardi, Tonia. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 37:11(2017), pp. 5651-5692. [10.3934/dcds.2017245]

Sign-changing tower of bubbles for a sinh-poisson equation with asymmetric exponents

Pistoia, Angela
;
2017

Abstract

Motivated by the statistical mechanics description of stationary 2D-turbulence, for a sinh-Poisson type equation with asymmetric nonlinearity, we construct a concentrating solution sequence in the form of a tower of singular Liouville bubbles, each of which has a different degeneracy exponent. The asymmetry parameter $γ∈(0, 1]$ corresponds to the ratio between the intensity of the negatively rotating vortices and the intensity of the positively rotating vortices. Our solutions correspond to a superposition of highly concentrated vortex configurations of alternating orientation; they extend in a nontrivial way some known results for $\gamma=1$. Thus, by analyzing the case $\gamma≠1$ we emphasize specific properties of the physically relevant parameter $\gamma$ in the vortex concentration phenomena.
2017
Asymmetric sinh-Poisson equation; Concentrating solution; Tower of bubbles; Analysis; Discrete Mathematics and Combinatorics; Applied Mathematics
01 Pubblicazione su rivista::01a Articolo in rivista
Sign-changing tower of bubbles for a sinh-poisson equation with asymmetric exponents / Pistoia, Angela; Ricciardi, Tonia. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 37:11(2017), pp. 5651-5692. [10.3934/dcds.2017245]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1072836
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