We address the question of well-posedness in spaces of analytic functions for the Cauchy problem for the hydrostatic incompressible Euler equations (inviscid primitive equations) on domains with boundary. By a suitable extension of the Cauchy-Kowalewski theorem we construct a locally in time, unique, real-analytic solution and give an explicit rate of decay of the radius of real-analyticity.
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Bounded domain
- Hydrostatic Euler equations
- Hydrostatic approximation
- Non-viscous primitive equations