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<p>We consider the free boundary problem for a layer of compressible barotropic fluid lying above a fixed bottom and below the atmosphere of positive constant pressure in the horizontally infinite setting. The fluid dynamics is governed by the compressible Euler equations with damping and gravity, and the effect of surface tension is neglected on the upper free boundary. We prove the global well-posedness of the problem near the equilibrium in both 2<i>D</i> and 3<i>D</i> and that the solution decays to the equilibrium at an algebraic rate.</p>

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Global Well-Posedness of Surface Waves for the Compressible Euler Equations with Damping

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Jiali Lian

摘要

We consider the free boundary problem for a layer of compressible barotropic fluid lying above a fixed bottom and below the atmosphere of positive constant pressure in the horizontally infinite setting. The fluid dynamics is governed by the compressible Euler equations with damping and gravity, and the effect of surface tension is neglected on the upper free boundary. We prove the global well-posedness of the problem near the equilibrium in both 2D and 3D and that the solution decays to the equilibrium at an algebraic rate.