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<p>We study, in this article, the stochastic Allen–Cahn–Navier–Stokes model in a bounded domain of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^{2}\)</EquationSource> </InlineEquation>. The model consists of the Navier–Stokes equations for the velocity, coupled with a Allen–Cahn model for the order (phase) parameter. We prove the regularity of the solutions in a higher space. The proof uses the It<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\hat{o}\)</EquationSource> </InlineEquation> formula and the energy method.</p>

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The regularity of the solutions for a stochastic 2D Allen–Cahn–Navier–Stokes model

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Salvador Awo Kougang,
  • Gabriel Deugoué,
  • Calvin Tadmon

摘要

We study, in this article, the stochastic Allen–Cahn–Navier–Stokes model in a bounded domain of \(\mathbb {R}^{2}\) . The model consists of the Navier–Stokes equations for the velocity, coupled with a Allen–Cahn model for the order (phase) parameter. We prove the regularity of the solutions in a higher space. The proof uses the It \(\hat{o}\) formula and the energy method.