Semigeostrophic equations in physical space with free upper boundary

Jingrui Cheng

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arXiv · 1501.06949

Semigeostrophic equations in physical space with free upper boundary

Jingrui Cheng

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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 $ν_0\in\mathcal{P}_2(\mathbf{R}^3)$ and is supported on $\{-\frac{1}δ\leq x_3\leq-δ\}$

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Jingrui Cheng. 2015-10-04. Semigeostrophic equations in physical space with free upper boundary. https://arxiv.org/abs/1501.06949

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