Abstract
We study the evolution of corner-like patch solutions to the generalized SQG equations. Depending on the angle size and order of the velocity kernel, the corner instantaneously bends either downward or upward. In particular, we obtain a new proof of the existence of strictly convex and smooth patch solutions which become immediately non-convex.
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Acknowledgements
JJ has been supported by NSF Grant DMS-1900943. IJ has been supported by the Samsung Science and Technology Foundation under Project Number SSTF-BA2002-04.
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Communicated by R. Shvydkoy.
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