Unique ergodicity in stochastic electroconvection

We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prove the existence and uniqueness of solutions, we define the corresponding Markov semigroup, and we study its Feller prope...

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Bibliographic Details
Published in:Nonlinear differential equations and applications 2024-07, Vol.31 (4), Article 65
Main Authors: Abdo, Elie, Glatt-Holtz, Nathan, Ignatova, Mihaela
Format: Article
Language:English
Subjects:
Analysis
Charge density
Mathematics
Mathematics and Statistics
Surface charge
Uniqueness
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Summary:We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prove the existence and uniqueness of solutions, we define the corresponding Markov semigroup, and we study its Feller properties. When the noise forces enough modes in phase space, we obtain the uniqueness of the smooth invariant measure for the Markov transition kernels associated with the model.
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-024-00954-3