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arXiv · 1808.07631

Global Solutions of a Surface Quasi-Geostrophic Front Equation

John K. Hunter·Jingyang Shu·Qingtian Zhang
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Abstract

We consider a nonlinear, spatially-nonlocal initial value problem in one space dimension on $\mathbb{R}$ that describes the motion of surface quasi-geostrophic (SQG) fronts. We prove that the initial value problem has a unique local smooth solution under a convergence condition on the multilinear expansion of the nonlinear term in the equation, and, for sufficiently smooth and small initial data, we prove that the solution is global.

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John K. Hunter, Jingyang Shu, Qingtian Zhang. 2018-08-23. Global Solutions of a Surface Quasi-Geostrophic Front Equation. https://doi.org/10.2140/paa.2021.3.403

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