1. Global solutions for a family of GSQG front equations.
- Author
-
Hunter, John K., Shu, Jingyang, and Zhang, Qingtian
- Subjects
EQUATIONS of motion ,NONLINEAR equations ,STATISTICAL smoothing ,EQUATIONS ,PARETO analysis ,EULER equations - Abstract
We prove the global existence of solutions with small and smooth initial data of a nonlinear dispersive equation for the motion of generalized surface quasi-geostrophic (GSQG) fronts in a parameter regime $ 1<\alpha<2 $, where $ \alpha = 1 $ corresponds to the SQG equation and $ \alpha = 2 $ corresponds to the incompressible Euler equations. This result completes previous global well-posedness results for $ 0<\alpha \le 1 $. We also use contour dynamics to derive the GSQG front equations for $ 1<\alpha<2 $. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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