Abstract
The semigeostrophic equations are used in meteorology. They appear as a variant of the two-dimensional Euler incompressible equations in vorticity form, where the Poisson equation that relates the stream function and the vorticity field is just replaced by the fully nonlinear elliptic Monge-Ampère equation. This work gathers new results concerning the semigeostrophic equations: existence and stability of measure-valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, and convergence to the incompressible Euler equations.
| Original language | English |
|---|---|
| Pages (from-to) | 795-823 |
| Number of pages | 29 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 38 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2006 |
| Externally published | Yes |
Keywords
- Monge-Ampère equations
- Optimal transportation
- Semigeostrophic equations