Time periodic solutions to the $2$D quasi-geostrophic equation with the supercritical dissipation

Mikihiro Fujii

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arXiv · 2006.03235

Time periodic solutions to the $2$D quasi-geostrophic equation with the supercritical dissipation

Mikihiro Fujii

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Abstract

We consider the $2$D dissipative quasi-geostrophic equation with the time periodic external force and prove the existence of a unique time periodic solution in the case of the supercritical dissipation. In this case, the smoothing effect of the semigroup generated by the dissipation term is too weak to control the nonlinearity in the Duhamel term of the correponding integral equation. In this paper, we give a new approach which does not depend on the contraction mapping principle for the integral equation.

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Mikihiro Fujii. 2020-06-05. Time periodic solutions to the $2$D quasi-geostrophic equation with the supercritical dissipation. https://arxiv.org/abs/2006.03235

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