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Wellposedness of inviscid SQG in the half-plane (2506.06601v1)
Published 7 Jun 2025 in math.AP
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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