On the well-posedness of the inviscid SQG equation

preprint2016arXivOpen access

In this paper we consider the inviscid SQG equation on the Sobolev spaces $H^s(\R^2)$ , $s > 2$ . Using a geometric approach we show that for any $T > 0$ the corresponding solution map, $θ(0) \mapsto θ(T)$ , is nowhere locally uniformly continuous.

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On the well-posedness of the inviscid SQG equation

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