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Unique ergodicity in stochastic electroconvection

Abdo, Elie
; 
Glatt-Holtz, Nathan
; 
Ignatova, Mihaela
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Journal article
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2024-05-15
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Mathematics
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https://scholarshare.temple.edu/handle/20.500.12613/12043
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https://doi.org/10.1007/s00030-024-00954-3
Abstract
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.
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Abdo, E., Glatt-Holtz, N. & Ignatova, M. Unique ergodicity in stochastic electroconvection. Nonlinear Differ. Equ. Appl. 31, 65 (2024). https://doi.org/10.1007/s00030-024-00954-3
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Springer Science and Business Media
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Nonlinear Differential Equations and Applications NoDEA, Vol. 31, Iss. 4
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