Scholarlink

<p>We consider the Cauchy problem of a compressible generic two-fluid model in three-dimensional space, and derive the global existence and uniqueness of strong solutions. The main challenge lies in the fact that the corresponding linear system of the model in Fourier variables has a zero eigenvalue. In addition to some usual smallness conditions, the smallness assumption of the <i>L</i><sup>1</sup>-norm of the initial perturbation plays an essential role in handling such a difficulty in the analysis of global solvability by Wu et al. (2024). In this paper, by exploiting the dissipation structure of the model and developing some new time-weighted estimates, the global solvability of the system is obtained without the technical <i>L</i><sup>1</sup> smallness condition. Furthermore, the <i>L</i><sup>2</sup>-<i>L</i><sup><i>p</i></sup> type decay-in-time rates of the solutions are shown.</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 solvability of a non-conservative compressible generic two-fluid model

  • 期刊论文

  • 发表日期：

    2026年3月4日

查看全文
  • Wenjun Wang,
  • Huanyao Wen

摘要

We consider the Cauchy problem of a compressible generic two-fluid model in three-dimensional space, and derive the global existence and uniqueness of strong solutions. The main challenge lies in the fact that the corresponding linear system of the model in Fourier variables has a zero eigenvalue. In addition to some usual smallness conditions, the smallness assumption of the L1-norm of the initial perturbation plays an essential role in handling such a difficulty in the analysis of global solvability by Wu et al. (2024). In this paper, by exploiting the dissipation structure of the model and developing some new time-weighted estimates, the global solvability of the system is obtained without the technical L1 smallness condition. Furthermore, the L2-Lp type decay-in-time rates of the solutions are shown.