Local existence of smooth solutions for the semigeostrophic equations on curved domains
Abstract
We prove local-in-time existence of smooth solutions to the semigeostrophic equations in the general setting of smooth, bounded and simply connected domains of $\mathbb{R}^2$ endowed with an arbitrary conformally flat metric and non-vanishing Coriolis term. We present a construction taking place in Eulerian coordinates, avoiding the classical reformulation in dual variables, used in the flat case with constant Coriolis force, but lacking in this general framework.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2022
- DOI:
- 10.48550/arXiv.2206.06191
- arXiv:
- arXiv:2206.06191
- Bibcode:
- 2022arXiv220606191S
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematical Physics
- E-Print:
- 18 pages