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Generalized Large Scale Semigeostrophic Equations: geometric structure and global well-posedness

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Mathematics for the Fluid Earth

Co-authors: Marcel Oliver (Jacobs University), Mahmut Calik (Jacobs University)

We derive and study a family of approximate Hamiltonian balance models (called GLSG ) for rotating shallow water in the semigeostrophic limit with spatially varying Coriolis parameter and non-trivial bottom topology. The models can be formulated in terms of an advected potential vorticity with a nonlinear vorticity inversion relation and include L_1 and LSG models proposed by R. Salmon as special cases.

We prove existence and uniqueness of global classical solutions to the GLSG equations for certain members of the family and study the PV invertibility as a function of the parameters.

This talk is part of the Isaac Newton Institute Seminar Series series.

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