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arXiv · 2212.00117

Well-posedness for the surface quasi-geostrophic front equation

Albert Ai·Ovidiu-Neculai Avadanei
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Abstract

We consider the well-posedness of the surface quasi-geostrophic (SQG) front equation. Hunter-Shu-Zhang [9] established well-posedness under a small data condition as well as a convergence condition on an expansion of the equation's nonlinearity. In the present article, we establish unconditional large data local well-posedness of the SQG front equation, while also improving the low regularity threshold for the initial data. In addition, we establish global well-posedness theory in the rough data regime by using the testing by wave packet approach of Ifrim-Tataru.

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Albert Ai, Ovidiu-Neculai Avadanei. 2022-11-30. Well-posedness for the surface quasi-geostrophic front equation. https://arxiv.org/abs/2212.00117

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