Well-posedness of stochastic mSQG equations with Kraichnan noise and $L^p$ data

Shuaijie Jiao; Dejun Luo

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arXiv · 2405.01045

Well-posedness of stochastic mSQG equations with Kraichnan noise and $L^p$ data

Shuaijie Jiao·Dejun Luo

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Abstract

We consider stochastic mSQG (modified Surface Quasi-Geostrophic) equations with multiplicative transport noise of Kraichnan type, and $L^p$-initial conditions. Inspired by the recent work of Coghi and Maurelli [arXiv:2308.03216], we show weak existence and pathwise uniqueness of solutions to the equations for suitable choices of parameters in the nonlinearity, the noise and the integrability of initial data.

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Shuaijie Jiao, Dejun Luo. 2024-05-02. Well-posedness of stochastic mSQG equations with Kraichnan noise and $L^p$ data. https://arxiv.org/abs/2405.01045

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