Kolloquien und Oberseminare Übersicht Detail

Vortragende Person/Vortragende Personen:
Jun.-Prof. Dr. Amru Hussein (Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau)

Abstract: The primitive equations are a fundamental geophysical model. Here, these equations subject to stochastic wind driven boundary conditions are studied. These boundary conditions on the atmosphere-ocean interface describe the balance of the shear stress of the ocean and the horizontal wind force. In contrast to previous works on deterministic wind driven boundary conditions described by Lions, Temam and Wang, we investigate for the first time stochastic wind driven boundary conditions. These stochastic wind driven boundary conditions are modeled by a cylindrical Wiener process. We adapt an approach by Da Prato and Zabczyk for stochastic boundary value problems to define a notion of solutions. Then a rigorous treatment of these stochastic boundary conditions, which combines stochastic and deterministic methods, yields that these equations admit a unique, local pathwise solution within the anisotropic L q t -H−1,p z L p xy-setting, where the ground space is weak in vertical z-direction and strong in horizontal xy-directions. This solution is constructed in critical spaces. This presentation is based on a joint work with Tim Binz , Matthias Hieber, Martin Saal (all from TU Darmstadt), see arxiv.org/abs/2009.09449