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In this paper, we prove local existence and uniqueness of analyticsharp-front solutions to a generalised SQG equation by the use of an abstractCauchy--Kowalevskaya theorem. Here, the velocity is determined by $u =|\nabla|^{-2\beta}\nabla^\perp\theta $ which (for $1<\beta\leq 2$) is moresingular than in SQG. This is achieved despite the appearance ofpseudodifferential operators of order higher than one in our equation, byrecasting our equation in a suitable integral form. We also provide a fullproof of the abstract version of the Cauchy--Kowalevskaya theorem we use.

Local Existence of Analytic Sharp Fronts for Singular SQG