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<p>We study in this paper a hyperbolic quasilinear formulation of the incompressible Navier–Stokes equations in two space dimensions, where we replace the classical Fourier’s law with a Cattaneo-type law. This innovative approach enables us to capture the effects of finite propagation speeds in fluid dynamics. We establish the global in time existence and uniqueness of solutions associated to a class of analytic initial data. Our findings contribute to a deeper understanding of fluid dynamics in hyperbolic contexts.</p>

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Global Existence for Hyperbolic Quasilinear Navier–Stokes Equations in the Gevrey Class

  • 期刊论文

  • 发表日期：

    2025年8月14日

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  • Bouthaina Abdelhedi,
  • Rim Farhat

摘要

We study in this paper a hyperbolic quasilinear formulation of the incompressible Navier–Stokes equations in two space dimensions, where we replace the classical Fourier’s law with a Cattaneo-type law. This innovative approach enables us to capture the effects of finite propagation speeds in fluid dynamics. We establish the global in time existence and uniqueness of solutions associated to a class of analytic initial data. Our findings contribute to a deeper understanding of fluid dynamics in hyperbolic contexts.