In this paper we consider the two-dimensional barotropic-vorticity equation in the first quadrant, and using a rearrangement variational principle, prove it has a solution. The solution represents a steady localized topographic ideal flow. The data given are the behavior of the flow at infinity, the rearrangement class of the vorticity field and the height of the localized seamount.
- Barotropic vorticity equation
- Semilinear elliptic equation
- Variational problems
ASJC Scopus subject areas
- Mathematics (all)