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<p>This manuscript investigates the three-dimensional stochastic compressible quantum magnetohydrodynamic equation with density-dependent and stochastic external forces. First, we approximate the modelled system. In this work, the existence of a martingale solution within a given time interval is established by deriving energy estimates and applying the fixed-point argument. The proposed system is approximated using the Faedo-Galerkin method, the Jakubowski-Skorokhod theorem, and the compactness method. Furthermore, the result is analyzed in the limit <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n \rightarrow \infty\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\eta \rightarrow 0\)</EquationSource> </InlineEquation>. Finally, numerical results for the quantum magnetohydrodynamic system are presented for the demonstrated theoretical findings.</p>

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Modeling and analysis of stochastic quantum magnetohydrodynamics equations with energy estimates

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月30日

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  • K. Divyabala,
  • N. Durga

摘要

This manuscript investigates the three-dimensional stochastic compressible quantum magnetohydrodynamic equation with density-dependent and stochastic external forces. First, we approximate the modelled system. In this work, the existence of a martingale solution within a given time interval is established by deriving energy estimates and applying the fixed-point argument. The proposed system is approximated using the Faedo-Galerkin method, the Jakubowski-Skorokhod theorem, and the compactness method. Furthermore, the result is analyzed in the limit \(n \rightarrow \infty\) and \(\eta \rightarrow 0\) . Finally, numerical results for the quantum magnetohydrodynamic system are presented for the demonstrated theoretical findings.