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arXiv · 1610.04764

Global in Time Classical Solutions to the 3D Quasi-geostrophic System for Large Initial Data

Matthew D. Novack·Alexis F. Vasseur
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Abstract

In this paper, the authors show the existence of global in time classical solutions to the 3D quasi-geostrophic system with Ekman pumping for any smooth initial value (possibly large). This system couples an inviscid transport equation in $\mathbb{R}^3_+$ with an equation on the boundary satisfied by the trace. The proof combines the De Giorgi regularization effect on the boundary $z=0$ -similar to the so called surface quasi-geostrophic equation- with Beale-Kato-Majda techniques to propagate regularity for $z>0$. A potential theory argument is used to strengthen the regularization effect on the trace up to the Besov space $\mathring{B}_{\infty,\infty}^1$.

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Matthew D. Novack, Alexis F. Vasseur. 2017-03-04. Global in Time Classical Solutions to the 3D Quasi-geostrophic System for Large Initial Data. https://doi.org/10.1007/s00220-017-3049-9

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