随机电对流中的独特遍历性

Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-05-15 DOI:10.1007/s00030-024-00954-3

Elie Abdo, Nathan Glatt-Holtz, Mihaela Ignatova

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引用次数: 0

摘要

我们考虑了一个随机电对流模型，该模型描述了二维流体中表面电荷密度的非线性演化，并带有加性随机强迫。我们证明了解的存在性和唯一性，定义了相应的马尔可夫半群，并研究了它的费勒特性。当噪声在相空间中施加了足够多的模式时，我们得到了与模型相关的马尔可夫转换核的平滑不变度量的唯一性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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 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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Nonlinear Differential Equations and Applications (NoDEA)

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