Abstract
By using Monge–Ampère geometry, we study the singular structure of a class of nonlinear Monge–Ampère equations in three dimensions, arising in geophysical fluid dynamics. We extend seminal earlier work on Monge–Ampère geometry by examining the role of an induced metric on Lagrangian submanifolds of the cotangent bundle. In particular, we show that the signature of the metric serves as a classification of the Monge–Ampère equation, while singularities and elliptic–hyperbolic transitions are revealed by degeneracies of the metric. The theory is illustrated by application to an example solution of the semigeostrophic equations.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
