Simply-connected vortex-patch shallow-water quasi-equilibria

A ‘‘vortex in cell” model for quasi-geostrophic, shallow water dynamics on the sphere

Article history: Received 15 July 2009 Received in revised form 29 December 2009 Accepted 4 January 2010 Available online 1 February 2010

The vortex patch problem for the surface quasi-geostrophic equation.

In this article, the analog of the Euler vortex patch problem for the surface quasi-geostrophic equation is considered.

Some results of semilocally simply connected property

If we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. In this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.

Investigating vortex dynamics in shallow water with topography

On Simply-connected 4-manifolds

This paper concerns (but does not succeed in performing) the diffeomorphism classification of closed, oriented, differential, simply-connected 4-manifolds. It arises out of the observation (due to Pontrjagin and Milnor [2]) that if two such manifolds Mx and M2 have isomorphic quadratic forms of intersection numbers on #2(Jft-), then there is a map / : M1-^-Mi which is a homotopy equivalence and...