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2. Local Well-Posedness of an Approximate Equation for SQG Fronts

Author

John K. Hunter, Qingtian Zhang, and Jingyang Shu

Subjects
Surface (mathematics), Physics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Mathematics::Analysis of PDEs, Approximate equation, Condensed Matter::Mesoscopic Systems and Quantum Hall Effect, Condensed Matter Physics, 01 natural sciences, 010305 fluids & plasmas, Sobolev space, Dispersive partial differential equation, Computational Mathematics, Nonlinear system, Mathematics - Analysis of PDEs, 0103 physical sciences, FOS: Mathematics, Initial value problem, 0101 mathematics, Mathematical Physics, Well posedness, Analysis of PDEs (math.AP)
Abstract

We prove local well-posedness in the Sobolev spaces $\dot H^s(\mathbb{T})$, with $s>7/2$, for an initial value problem for a nonlocal, cubically nonlinear, dispersive equation that provides an approximate description of the evolution of surface quasi-geostrophic (SQG) fronts with small slopes., 18 pages, 1 figure

Published
2018
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