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arXiv · 2506.06601

Wellposedness of inviscid SQG in the half-plane

In-Jee Jeong·Junha Kim·Hideyuki Miura
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Abstract

We consider the SQG equation without dissipation on the half-plane with Dirichlet boundary condition, and prove local wellposedness in the spaces $W^{3,p}$ and $C^{2,\beta}$ for any $1<p<\infty$ and $0<\beta<1$. We complement this wellposedness by showing that for generic $C^{\infty}_{0}$ initial data, the unique corresponding solution does not belong to $W^{3,\infty}$.

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In-Jee Jeong, Junha Kim, Hideyuki Miura. 2025-06-07. Wellposedness of inviscid SQG in the half-plane. https://arxiv.org/abs/2506.06601

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