On the unique ergodicity for a class of 2 dimensional stochastic wave equations

Justin Forlano; Leonardo Tolomeo

doi:10.1090/tran/8973

On the unique ergodicity for a class of 2 dimensional stochastic wave equations

Justin Forlano, Leonardo Tolomeo

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We study the global-in-time dynamics for a stochastic semilinear wave equation with cubic defocusing nonlinearity and additive noise, posed on the 2-dimensional torus. The noise is taken to be slightly more regular than space-time white noise. In this setting, we show existence and uniqueness of an invariant measure for the Markov semigroup generated by the flow over an appropriately chosen Banach space. This extends a result of the second author [Comm. Math. Phys. 377 (2020), pp. 1311–1347] to a situation where the invariant measure is not explicitly known.

Original language	English
Pages (from-to)	345-394
Number of pages	50
Journal	Transactions of the American Mathematical Society
Volume	377
Early online date	6 Oct 2023
DOIs	https://doi.org/10.1090/tran/8973
Publication status	Published - Jan 2024

Keywords

ergodicity
invariant measure
Stochastic nonlinear wave equation
white noise

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/tran/8973

Cite this

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abstract = "We study the global-in-time dynamics for a stochastic semilinear wave equation with cubic defocusing nonlinearity and additive noise, posed on the 2-dimensional torus. The noise is taken to be slightly more regular than space-time white noise. In this setting, we show existence and uniqueness of an invariant measure for the Markov semigroup generated by the flow over an appropriately chosen Banach space. This extends a result of the second author [Comm. Math. Phys. 377 (2020), pp. 1311–1347] to a situation where the invariant measure is not explicitly known.",

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AB - We study the global-in-time dynamics for a stochastic semilinear wave equation with cubic defocusing nonlinearity and additive noise, posed on the 2-dimensional torus. The noise is taken to be slightly more regular than space-time white noise. In this setting, we show existence and uniqueness of an invariant measure for the Markov semigroup generated by the flow over an appropriately chosen Banach space. This extends a result of the second author [Comm. Math. Phys. 377 (2020), pp. 1311–1347] to a situation where the invariant measure is not explicitly known.

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KW - invariant measure

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KW - white noise

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On the unique ergodicity for a class of 2 dimensional stochastic wave equations

Abstract

Keywords

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