Stochastic Geophysical Fluid Dynamics

This book is based on an Oberwolfach Seminar, and it intends to give an introduction and an overview to several directions of the recent research on stochastic geophysical fluid dynamics and to discuss different geophysical stochastic partial differential equations.

Introduction and an overview to several directions of the recent research on stochastic geophysical fluid dynamics Discussion of the origins and forms of noise in geophysical fluid dynamics Discussion of different geophysical stochastic partial differential equations

Autorentext

Franco Flandoli is full professor in probability and statistics at the Scuola Normale Superiore of Pisa. Before he has been professor at the universities of Torino and Pisa. His main research fields are stochastic ordinary and partial differential equations, stochastic models in fluid dynamics, random dynamical systems, and macroscopic limits of particle systems. He has been lecturer of CIME Summer School 2008 and Saint Flor Summer School 2010. He runs an ERC advanced Grant on Noisy Fluids.

Darryl Holm is a Professor of Applied Mathematics at Imperial College London and a Laboratory Fellow in the Theoretical Division and the Computation and Computer Science Division at Los Alamos National Laboratory. His main research field is Stochastic Geometric Mechanics. He is a Principal Investigator for the ERC Synergy Grant on Stochastic Transport in Upper Ocean Dynamics (STUOD).

Amru Hussein is a Professor at the University of Kaiserslautern-Landau. He is a member of the functional analysis and stochastic analysis research group, and his research focuses on functional analysis and partial differential equations.

Martin Saal was a researcher at the Technical University of Darmstadt. His research focused on deterministic and stochastic partial differential equations, and applications to mathematical fluid mechanics. He works for an insurance company.

Inhalt

• Stochastic Fluid Mechanics and Boussinesq Hypothesis.- Scaling Limit of 2D Euler to NavierStokes.- From Additive to Transport Noise in 3D Navier-Stokes Equations.- On the Role of Lp (Lq)-Techniques in Regularization by Noise of Reaction-Diffusion Equations.- Well-Posedness and Inviscid Limit Results for Stochastic Second-Grade Fluid Equations with Transport Noise in Bounded Domains.- The Stochastic Primitive Equations.- Stochastic Geometric Fluid Dynamics.