Stochastic one layer shallow water equations with Lévy noise

Abstract

This work investigates the existence of both martingale and pathwise solutions of the single layer shallow water equations on a bounded domain \begin{document}$ \mathcal{M} \subset \mathbb{R}^2 $\end{document} perturbed by a Levy noise which may represent bursts of surface winds. The construction of both solutions are based on some truncation, the classical Faedo-Galerkin approximation scheme, a modified version of the Skorokhod representation theorem, stopping time arguments and anisotropic estimates.