Local Regularity for the Modified SQG Patch Equation
نویسندگان
چکیده
منابع مشابه
Local regularity for the modified SQG patch equation
We study the patch dynamics for a family of active scalars called modified SQG equations, on the whole plane and on the half-plane. These involve a parameter α which appears in the power of the kernel in their Biot-Savart laws and describes the degree of regularity of the equation. The values α = 0 and α = 1 2 correspond to the 2D Euler and SQG equations, respectively. We establish here local-i...
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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 law which is one derivative less regular than in the Euler case, and the question of global regularity for its solutions is still open. We study here the patch dynamics in the half-plane for a family of active scalars...
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2016
ISSN: 0010-3640
DOI: 10.1002/cpa.21677