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

Angela Pistoia; Tonia Ricciardi

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arXiv · 1606.07724

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

Angela Pistoia·Tonia Ricciardi

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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 $\gamma\in(0,1]$ 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 $\gamma\neq1$ we emphasize specific properties of the physically relevant parameter $\gamma$ in the vortex concentration phenomena.

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Angela Pistoia, Tonia Ricciardi. 2016-06-24. Sign-changing tower of bubbles for a sinh-Poisson equation with asymmetric exponents. https://arxiv.org/abs/1606.07724

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