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math.AP2015★ 15 cited
Finite time singularity formation for the modified SQG patch equation
Alexander Kiselev, Lenya Ryzhik, Yao Yao +1
It is well known that the incompressible Euler equations in two dimensions have globally regular solutions. The inviscid surface quasi-geostrophic (SQG) equation has a Biot-Savart…
math.AP2015
Local regularity for the modified SQG patch equation
Alexander Kiselev, Yao Yao, Andrej Zlatos
We study the patch dynamics on the whole plane and on the half-plane for a family of active scalars called modified SQG equations. These involve a parameter which appears in th…