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<p>This work investigates the stochastic rotation-two-component Camassa–Holm system on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">R</mi> </math></EquationSource> </InlineEquation>. The noise structure combines classical transport-type noise and Itô-type multiplicative noise. Furthermore, the system is examined under asymptotic conditions as <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(x \rightarrow \infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo stretchy="false">→</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>, which are more physically realistic compared to existing results in the literature. First, we establish the existence, uniqueness, and blow-up criterion for pathwise classical solutions. Subsequently, we prove that sufficiently fast-growing noise ensures global regularity.</p>

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On the pathwise classical solutions to the stochastic rotation-two-component Camassa–Holm system

  • 期刊论文

  • 发表日期：

    2025年11月30日

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  • Yingting Miao

摘要

This work investigates the stochastic rotation-two-component Camassa–Holm system on \(\mathbb {R}\) R . The noise structure combines classical transport-type noise and Itô-type multiplicative noise. Furthermore, the system is examined under asymptotic conditions as \(x \rightarrow \infty \) x → ∞ , which are more physically realistic compared to existing results in the literature. First, we establish the existence, uniqueness, and blow-up criterion for pathwise classical solutions. Subsequently, we prove that sufficiently fast-growing noise ensures global regularity.