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<p>In this paper, we study the global dynamics of the 3D compressible Euler–Poisson–Korteweg equations. We would firstly establish the global well-posedness and scattering. Moreover, we will show the vanishing capillarity limit for the solution, which indicates the solution of Euler–Poisson–Korteweg equations would converge to the ones of Euler–Poisson equations. Our strategy combines energy estimates, dispersive estimates and space-time resonance analysis with delicate capillarity parameter estimates.</p>

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Global dynamics and vanishing capillarity limit of the 3D Euler–Poisson–Korteweg equations

  • 期刊论文

  • 发表日期：

    2025年4月9日

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  • Zihao Song

摘要

In this paper, we study the global dynamics of the 3D compressible Euler–Poisson–Korteweg equations. We would firstly establish the global well-posedness and scattering. Moreover, we will show the vanishing capillarity limit for the solution, which indicates the solution of Euler–Poisson–Korteweg equations would converge to the ones of Euler–Poisson equations. Our strategy combines energy estimates, dispersive estimates and space-time resonance analysis with delicate capillarity parameter estimates.