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Global solutions of a
surface quasigeostrophic front equation
John K. Hunter, Jingyang Shu and Qingtian Zhang |
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Vol. 3 (2021), No. 3, 403–472
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DOI: 10.2140/paa.2021.3.403
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Abstract |
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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. |
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Keywords
surface quasigeostrophic equation, surface waves, nonlinear
dispersive waves, global solutions
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Mathematical Subject Classification
Primary: 35Q35, 35Q86
Secondary: 86A10
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Milestones
Received: 24 November 2019
Revised: 23 June 2021
Accepted: 21 August 2021
Published: 12 September 2021
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Authors |
| John K. Hunter | |
| Department of Mathematics University of California Davis, CA United States |
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| Jingyang Shu | |
| Department of Mathematics Temple University Philadelphia, PA United States |
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| Qingtian Zhang | |
| Department of Mathematics West Virginia University Morgantown, WV United States |
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