Scholarlink

<p>In this article, we are concerned with the global existence and time-asymptotic stability of strong solutions to the outflow problem of the one-dimensional isentropic compressible Navier-Stokes-Korteweg system with <i>γ</i>-law type pressure and power like density-dependent viscosity and capillarity in the half-space ℝ<sup>+</sup>. Under certain requirements on the spatial asymptotic states and boundary data, the time-asymptotic profile of this problem is the 2-rarefaction wave of the corresponding Euler system. By employing the elementary <i>L</i><sup>2</sup>-energy method together with Kanel’s technique, we prove that this 2-rarefaction wave is time-asymptotically nonlinear stable provided that the pressure, viscosity and capillarity satisfy some structural conditions. Here both the initial perturbation and the strength of the rarefaction wave can be arbitrarily large.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Global stability of rarefaction wave to the outflow problem of the one-dimensional compressible Navier-Stokes-Korteweg system

  • 期刊论文

  • 发表日期：

    2026年5月9日

查看全文
  • Fanfan Jiang,
  • Zhengzheng Chen

摘要

In this article, we are concerned with the global existence and time-asymptotic stability of strong solutions to the outflow problem of the one-dimensional isentropic compressible Navier-Stokes-Korteweg system with γ-law type pressure and power like density-dependent viscosity and capillarity in the half-space ℝ+. Under certain requirements on the spatial asymptotic states and boundary data, the time-asymptotic profile of this problem is the 2-rarefaction wave of the corresponding Euler system. By employing the elementary L2-energy method together with Kanel’s technique, we prove that this 2-rarefaction wave is time-asymptotically nonlinear stable provided that the pressure, viscosity and capillarity satisfy some structural conditions. Here both the initial perturbation and the strength of the rarefaction wave can be arbitrarily large.