Global regularity and decay behavior for Leray equations with critical-dissipation and its application to self-similar solutions

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2024-02-29 DOI:10.1090/tran/9148

Changxing Miao, Xiaoxin Zheng

引用次数: 0

Abstract

In this paper, we show the global regularity and the optimal decay of weak solutions to the generalized Leray problem with critical dissipation. Our approach hinges on the maximal smoothing effect, L p L^{p} -type elliptic regularity of linearization, and the action of the heat semigroup generated by the fractional powers of Laplace operator on distributions with Fourier transforms supported in an annulus. As a by-product, we construct a self-similar solution to the three-dimensional incompressible Navier-Stokes equations. Most notably, we prove the global regularity and the optimal decay without the need for additional requirements found in existing literatures.

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具有临界消散的勒雷方程的全局正则性和衰减行为及其在自相似解中的应用

在本文中，我们展示了具有临界耗散的广义勒雷问题的全局正则性和弱解的最优衰减。我们的方法依赖于最大平滑效应、线性化的 L p L^{p} 型椭圆正则性以及热半定理的作用。 -线性化的椭圆正则性，以及拉普拉斯算子的分数幂所产生的热半群对傅里叶变换支持在环面上的分布的作用。作为副产品，我们构建了三维不可压缩纳维-斯托克斯方程的自相似解。最值得注意的是，我们证明了全局正则性和最优衰减，而无需现有文献中的额外要求。

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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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.