非晶分子束外延模型弱解的部分正则性

IF 0.8 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2023-11-15 DOI:10.1007/s10114-023-2458-2

Yan Qing Wang, Yi Ke Huang, Gang Wu, Dao Guo Zhou

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引用次数: 0

摘要

本文研究了下述抛物方程$${h_t} + {h_{xxxx}} + {\partial _{xx}}|{h_x}{|^\alpha } = f.$$中合适弱解的可能奇异点集${\cal S}$的Hausdorff维数与非线性项参数α之间的精确关系。结果表明，当$5/3 \le \alpha < 7/3$时，${\cal S}$的${{3\alpha - 5} \over {\alpha - 1}}$维抛物Hausdorff维数为零，推广了Ozánski和Robinson在[SIAM J. Math]中最近的相应工作。分析的[j] .中国科学:自然科学，2016,38(1):1 - 2。同样的结果也适用于三维修正的Navier-Stokes系统。

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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Partial Regularity of Suitable Weak Solutions of the Model Arising in Amorphous Molecular Beam Epitaxy

In this paper, we are concerned with the precise relationship between the Hausdorff dimension of possible singular point set ${\cal S}$ of suitable weak solutions and the parameter α in the nonlinear term in the following parabolic equation

$${h_t} + {h_{xxxx}} + {\partial _{xx}}|{h_x}{|^\alpha } = f.$$

It is shown that when $5/3 \le \alpha < 7/3$, the ${{3\alpha - 5} \over {\alpha - 1}}$ dimensional parabolic Hausdorff measure of ${\cal S}$ is zero, which generalizes the recent corresponding work of Ozánski and Robinson in [SIAM J. Math. Anal., 51, 228–255 (2019)] for α = 2 and f = 0. The same result is valid for a 3D modified Navier–Stokes system.

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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.