mSQG equations in distributional spaces and point vortex approximation

Franco Flandoli; Martin Saal

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arXiv · 1812.05361

mSQG equations in distributional spaces and point vortex approximation

Franco Flandoli·Martin Saal

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Abstract

Existence of distributional solutions of a modified Surface Quasi-Geostrophic equation (mSQG) is proven for $\mu$-almost every initial condition, where $\mu$ is a suitable Gaussian measure. The result is the by-product of existence of a stationary solution with white noise marginal. This solution is constructed as a limit of random point vortices, uniformly distributed and rescaled according to the Central Limit Theorem.

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Franco Flandoli, Martin Saal. 2018-12-13. mSQG equations in distributional spaces and point vortex approximation. https://arxiv.org/abs/1812.05361

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