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<p>We show that the 1D Hou–Luo model on the real line admits exact self-similar finite-time blowup solutions with smooth self-similar profiles. The existence of these profiles is established via a fixed-point method that is purely analytic. We also prove that the profiles satisfy some monotonicity and convexity properties that were unknown before, and we give rigorous estimates on the algebraic decay rates of the profiles in the far field. Our result supplements the previous computer-assisted proof of self-similar finite-time blowup for the Hou–Luo model with finer characterizations of the profiles.</p>

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Exact Self-Similar Finite-Time Blowup of the Hou–Luo Model with Smooth Profiles

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • De Huang,
  • Xiang Qin,
  • Xiuyuan Wang,
  • Dongyi Wei

摘要

We show that the 1D Hou–Luo model on the real line admits exact self-similar finite-time blowup solutions with smooth self-similar profiles. The existence of these profiles is established via a fixed-point method that is purely analytic. We also prove that the profiles satisfy some monotonicity and convexity properties that were unknown before, and we give rigorous estimates on the algebraic decay rates of the profiles in the far field. Our result supplements the previous computer-assisted proof of self-similar finite-time blowup for the Hou–Luo model with finer characterizations of the profiles.