光滑型侯-罗模型的精确自相似有限时间爆破

IF 2.6 1区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Mathematical Physics Pub Date : 2025-09-01 DOI:10.1007/s00220-025-05429-9

De Huang, Xiang Qin, Xiuyuan Wang, Dongyi Wei

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引用次数: 0

摘要

我们证明了实线上的一维侯罗模型具有光滑自相似轮廓的精确自相似有限时间爆破解。通过一种纯解析的不动点法确定了这些曲线的存在性。我们还证明了这些剖面满足一些以前不知道的单调性和凸性，并给出了这些剖面在远场的代数衰减率的严格估计。我们的结果补充了先前的计算机辅助证明的自相似有限时间爆破的侯-罗模型与更精细的特征剖面。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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.

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来源期刊

Communications in Mathematical Physics 物理-物理：数学物理

CiteScore

4.70

自引率

8.30%

发文量

226

审稿时长

3-6 weeks

期刊介绍： The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.