Local Well-posedness of Two Dimensional SQG Equation and Related Models
Abstract
In this paper, we present a new and elementary proof of the local existence and uniqueness of the classical solution to the Cauchy problem of the two-dimensional generalized surface quasi-geostrophic (SQG) equation via the method of the contraction mapping principle. Also, same result holds true for a kind of transport equation with nonlocal velocity via the method of the contraction mapping principle.
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