Smooth solutions of the surface semi-geostrophic equations

Stefania Lisai*, Mark Wilkinson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The semi-geostrophic equations have attracted the attention of the physical and mathematical communities since the work of Hoskins in the 1970s owing to their ability to model the formation of fronts in rotation-dominated flows, and also to their connection with optimal transport theory. In this paper, we study an active scalar equation, whose activity is determined by way of a Neumann-to-Dirichlet map associated to a fully nonlinear second-order Neumann boundary value problem on the infinite strip R2× (0 , 1) , that models a semi-geostrophic flow in regime of constant potential vorticity. This system is an expression of an Eulerian semi-geostrophic flow in a coordinate system originally due to Hoskins, to which we shall refer as Hoskins’ coordinates. We obtain results on the local-in-time existence and uniqueness of classical solutions of this active scalar equation in Hölder spaces.

Original languageEnglish
Article number16
JournalCalculus of Variations and Partial Differential Equations
Issue number1
Early online date3 Dec 2019
Publication statusPublished - Feb 2020

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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