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<p>We prove the existence of a global martingale solution of a stochastic electroconvection equations on <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10306_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {R}}^2\)</EquationSource> </InlineEquation> 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 <i>qRq</i> which makes the equations strongly nonlinear.</p>

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

  • 期刊论文

  • 发表日期：

    2025年8月22日

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  • Gaocheng Yue

摘要

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.