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<p>In this paper, we study the Cauchy–Dirichlet problem for the equation with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(x-\)</EquationSource> </InlineEquation>dependent coefficients modelling the Couette flow of fractional viscoelastic fluid. First, based on the asymptotic behavior on the multivariate Mittag-Leffler functions, we introduce the definition of mild solutions of the problem. Next, we prove the unique existence and the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(H^2-\)</EquationSource> </InlineEquation>regularity of the mild solution under some suitable conditions. Finally, the long time behavior of the mild solution is obtained by using the Laplace transform technique.</p>

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Initial-boundary value problems for equations of motion of viscoelastic fluid with fractional derivatives

  • 期刊论文

  • 发表日期：

    2025年10月17日

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  • Chung-Sik Sin,
  • Kwon Ho

摘要

In this paper, we study the Cauchy–Dirichlet problem for the equation with \(x-\) dependent coefficients modelling the Couette flow of fractional viscoelastic fluid. First, based on the asymptotic behavior on the multivariate Mittag-Leffler functions, we introduce the definition of mild solutions of the problem. Next, we prove the unique existence and the \(H^2-\) regularity of the mild solution under some suitable conditions. Finally, the long time behavior of the mild solution is obtained by using the Laplace transform technique.