Stochastic one layer shallow water equations with Lévy noise

Justin Cyr; Phuong Nguyen; Roger Temam

doi:10.3934/dcdsb.2018331

Article Contents

2019, Volume 24, Issue 8: 3765-3818. Doi: 10.3934/dcdsb.2018331

This issue Previous Article A new proof of the competitive exclusion principle in the chemostat Next Article The Magneto–Hydrodynamic equations: Local theory and blow-up of solutions

Stochastic one layer shallow water equations with Lévy noise

Department of Mathematics and The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN 47405, USA

* Corresponding author: Roger Temam
* Corresponding author: Roger Temam

Dedicated to Peter Eris Kloeden on the occasion of his 70^th birthday

Received: December 2017

Revised: May 2018

Early access: January 4, 2019

Published online: January 4, 2019

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Abstract

This work investigates the existence of both martingale and pathwise solutions of the single layer shallow water equations on a bounded domain $ \mathcal{M} \subset \mathbb{R}^2 $ perturbed by a Lévy 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.

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Mathematics Subject Classification: Primary: 35R60, 60H15.

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