Year: 2026
Type: article
Abstract: This article considers the variational wave equation with viscosity and transport noise as a system of three coupled nonlinear stochastic partial differential equations. We prove pathwise global existence, uniqueness, and temporal continuity of solutions to this system in $$L^2_x$$ L x 2 . Martingale solutions are extracted from a two-level Galerkin approximation via the Skorokhod–Jakubowski theorem. We use the apparatus of Dudley maps to streamline this stochastic compactness method, bypassing the usual martingale identification argument. Pathwise uniqueness for the system is established through a renormalisation procedure that involves double commutator estimates and a delicate handling of noise and nonlinear terms. New model-specific commutator estimates are proven.
Author: Peter H. C. Pang
Institution: University of Oslo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Award: G7910507305
OpenAlex ID: W7118268790