Semigeostrophic equations in physical space with free upper boundary

Abstract

We define various notions of Lagrangian solution in physical space for 3-d incompressible geostrophic system with free upper boudary under different conditions for initial data,then prove their existence via the minimization with respect to a geostrophic functional.As a byproduct of our proof,we obtain the existence of measure-valued dual space solutions when the initial measure ${\nu }_0\in {\mathcal{P}}_2({\mathbf{R}}^3)$ and is supported on $\{-\frac{1}{\delta }\le x_3\le -\delta \}$

47 pages

References in corpus (1)

• Free upper boundary value problems for the semi-geostrophic equations