Year: 2024
Type: preprint
Abstract: We establish general quantitative conditions for stochastic evolution equations with locally monotone drift and degenerate additive Wiener noise in variational formulation resulting in the existence of a unique invariant probability measure for the associated exponentially ergodic Markovian Feller semigroup. We prove improved moment estimates for the solutions and the $e$-property of the semigroup. Furthermore, we provide quantitative upper bounds for the $2$-Wasserstein $\varepsilon$-mixing times. Examples on possibly unbounded domains include the stochastic incompressible 2D Navier-Stokes equations, shear thickening stochastic power-law fluid equations, the stochastic heat equation, as well as, stochastic semilinear equations such as the 1D stochastic Burgers equation.
Source: arXiv (Cornell University)
Authors: Barrera, Gerardo, Tölle, Jonas M.
Institutions: University of Lisbon, Instituto Superior Técnico, Aalto University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405034095