2024
DOI: 10.3934/dcds.2024053
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Construction of unstable concentrated solutions of the Euler and gSQG equations

Martin Donati

Abstract: In this paper we construct solutions to the Euler and gSQG equations that are concentrated near unstable stationary configurations of pointvortices. Those solutions are themselves unstable, in the sense that their localization radius grows from order ε to order ε β (with β < 1) in a time of order | ln ε|. In particular, this proves that the logarithmic lower-bound obtained in previous papers (in particular [P. Buttà and C. Marchioro, Long time evolution of concentrated Euler flows with planar symmetry, SIAM J.… Show more

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