Incompressible Euler equations with stochastic forcing: A geometric approach
Artikel i vetenskaplig tidskrift, 2023

We consider a stochastic version of Euler equations using the infinite-dimensional geometric approach as pioneered by Ebin and Marsden (1970). For the Euler equations on a compact manifold (possibly with smooth boundary) we establish local existence and uniqueness of a strong solution in spaces of Sobolev mappings (of high enough regularity). Our approach combines techniques from stochastic analysis and infinite-dimensional geometry and provides a novel toolbox to establish local well-posedness of stochastic non-linear partial differential equations.

Ebin–Marsden theory

half-Lie group

Stochastic integration on Hilbert manifolds

Stochastic Euler equation

Manifold of Sobolev mappings

Författare

Mario Maurelli

Universita di Pisa

Klas Modin

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Alexander Schmeding

Nord universitet

Stochastic Processes and their Applications

0304-4149 (ISSN)

Vol. 159 101-148

Geometriska numeriska metoder för beräkningsanatomi

Vetenskapsrådet (VR) (2017-05040), 2018-01-01 -- 2021-12-31.

CHallenges in Preservation of Structure (CHiPS)

Europeiska kommissionen (EU) (EC/H2020/691070), 2016-01-01 -- 2019-12-31.

Ämneskategorier

Beräkningsmatematik

Geometri

Matematisk analys

DOI

10.1016/j.spa.2023.01.011

Mer information

Senast uppdaterat

2023-02-16