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<p>This paper is concerned with the global existence and asymptotic behavior of solutions to the compressible Hookean viscoelastic fluid system in three-dimensional (3D) bounded domains with no-slip boundary conditions. By reformulating the problem in Lagrangian coordinates, we prove the existence of a unique global strong solution for some classes of large initial data, provided the elastic coefficient <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\kappa \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>κ</mi> </math></EquationSource> </InlineEquation> is sufficiently large relative to the initial perturbation. Furthermore, we demonstrate the exponential time-decay of solutions toward equilibrium. Additionally, we show that for sufficiently large elastic coefficients, the solutions of the nonlinear system converge to those of the corresponding linearized problem at an algebraic rate in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\kappa \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>κ</mi> </math></EquationSource> </InlineEquation>. To address the analytical challenges posed by boundary in establishing higher-order derivative estimates, we employ geometric techniques introduced by Christodoulou and Lindblad [<CitationRef CitationID="CR4">4</CitationRef>].</p>

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Global solutions for compressible Hookean viscoelastic fluids with some classes of large initial data in bounded domains

  • 期刊论文

  • 发表日期：

    2026年7月8日

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  • Youyi Zhao,
  • Deguo Zou

摘要

This paper is concerned with the global existence and asymptotic behavior of solutions to the compressible Hookean viscoelastic fluid system in three-dimensional (3D) bounded domains with no-slip boundary conditions. By reformulating the problem in Lagrangian coordinates, we prove the existence of a unique global strong solution for some classes of large initial data, provided the elastic coefficient \(\kappa \) κ is sufficiently large relative to the initial perturbation. Furthermore, we demonstrate the exponential time-decay of solutions toward equilibrium. Additionally, we show that for sufficiently large elastic coefficients, the solutions of the nonlinear system converge to those of the corresponding linearized problem at an algebraic rate in \(\kappa \) κ . To address the analytical challenges posed by boundary in establishing higher-order derivative estimates, we employ geometric techniques introduced by Christodoulou and Lindblad [4].