Work

Weak and strong solutions to nonlinear SPDEs with unbounded noise

Year: 2024

Type: article

Abstract: We introduce an extended variational framework for nonlinear SPDEs with unbounded noise, defining three different solution types of increasing strength along with criteria to establish their existence. The three notions can be understood as probabilistically and analytically weak, probabilistically strong and analytically weak, as well as probabilistically and analytically strong. Our framework facilitates several well-posedness results for the Navier–Stokes Equation with transport noise, equipped with the no-slip and Navier boundary conditions.

Source: Nonlinear Differential Equations and Applications NoDEA

DOI: 10.1007/s00030-024-00993-w

Author: Daniel Goodair

Institutions: Imperial College London, École Polytechnique Fédérale de Lausanne

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Imperial College London, Engineering and Physical Sciences Research Council