Cullen, M. J. P.; Douglas, Robert J.; Roulston, I.; Sewell, M. J.(2005-05-25)

It is shown that the solution of the semi-geostrophic equations for shallow-water flow can be found and analysed in spherical geometry by methods similar to those used in the existing $f$-plane solutions. Stable states in ...

It is shown how large-amplitude stability results for flows governed by potential-vorticity conservation can be obtained by geometric arguments using rearrangements of functions. The method allows for non-smooth solutions, ...

This paper proves some results concerning the polar factorisation of an integrable vector-valued function $u$ into the composition $u = u^{\#} \circ s$, where $u^{\#} = \nabla \psi$ almost everywhere for some convex function ...

This paper proves some results concerning the polar factorisation of an integrable vector-valued function $u$ into the composition $u = u^{\#} \circ s$, where $u^{\#}$ is equal almost everywhere to the gradient of a convex ...