Kolloquien und Oberseminare Übersicht Detail

Vortragende Person/Vortragende Personen:
Dr. Lucio Galeati (EPFL Lausanne)

In recent years, several authors have studied solution properties of 2D Euler equations in the presence of an additional stochastic transport term; this perturbation aims at representing endogenously the unresolved fast sub-grid scales of the fluid, and is justified by Euler-Poincar´e type variational principles. We will assume the stochastic perturbation to be driven by a geometric p-variation rough path, for some p ∈ [2, 3); this includes the classical Stratonovich Brownian noise. We are able to show existence and uniqueness of solutions for a general class of nonlinear rough continuity equation on R d (including 2D vorticity Euler as a special case), for initial data in L 1 ∩ L∞. The proof relies on a combination of rough paths and unbounded rough drivers techniques, DiPerna-Lions type arguments and Lagrangian representations.

Based on ongoing joint work with James Micheal Lehay (Imperial College) and Torstein Nilssen (Agder).