Vol. 3, No. 3, 2021

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Global solutions of a surface quasigeostrophic front equation

John K. Hunter, Jingyang Shu and Qingtian Zhang

Vol. 3 (2021), No. 3, 403–472
DOI: 10.2140/paa.2021.3.403
Abstract

We consider a nonlinear, spatially nonlocal initial value problem in one space dimension on that describes the motion of surface quasigeostrophic (SQG) fronts. We prove that the initial value problem has a unique local smooth solution under a convergence condition on the multilinear expansion of the nonlinear term in the equation, and, for sufficiently smooth and small initial data, we prove that the solution is global.

Keywords
surface quasigeostrophic equation, surface waves, nonlinear dispersive waves, global solutions
Mathematical Subject Classification
Primary: 35Q35, 35Q86
Secondary: 86A10
Milestones
Received: 24 November 2019
Revised: 23 June 2021
Accepted: 21 August 2021
Published: 12 September 2021
Authors
John K. Hunter
Department of Mathematics
University of California
Davis, CA
United States
Jingyang Shu
Department of Mathematics
Temple University
Philadelphia, PA
United States
Qingtian Zhang
Department of Mathematics
West Virginia University
Morgantown, WV
United States