具有乘性噪声的\({\mathbb {R}}^2\)上随机电对流方程的鞅解

IF 1.7 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-08-22 DOI:10.1007/s00245-025-10306-x

Gaocheng Yue

引用次数: 0

摘要

证明了\({\mathbb {R}}^2\)上一类具有乘性噪声的随机电对流方程全局鞅解的存在性。该证明基于随机紧性方法和Skorokhod定理的Jakubowski推广。主要的困难是非线性项qRq使方程成为强非线性。

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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Martingale Solutions of the Stochastic Electroconvection Equations on \({\mathbb {R}}^2\) with Multiplicative Noise

We prove the existence of a global martingale solution of a stochastic electroconvection equations on \({\mathbb {R}}^2\) with multiplicative noise. The proof is based on the stochastic compactness method and the Jakubowski generalization of the Skorokhod theorem. The main difficulty is caused by the nonlinearity term qRq which makes the equations strongly nonlinear.

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.