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

被引：1

作者：

Wang, Yan Qing ^{[1
]}

Huang, Yi Ke ^{[1
]}

Wu, Gang ^{[2
]}

Zhou, Dao Guo ^{[3
]}

机构：

[1] Zhengzhou Univ Light Ind, Coll Math & Informat Sci, Zhengzhou 450002, Peoples R China

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[3] Hangzhou Normal Univ, Sch Math, Hangzhou 311121, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2023年 / 39卷 / 11期

关键词：

Surface growth model; modified Navier-Stokes equations; partial regularity; Hausdorff dimension; PARABOLIC-SYSTEMS; GLOBAL-SOLUTIONS; GROWTH; PROOF; CONSERVATION; EXISTENCE; EQUATIONS;

D O I：

10.1007/s10114-023-2458-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with the precise relationship between the Hausdorff dimen-sion of possible singular point set S of suitable weak solutions and the parameter alpha in the nonlinear term in the following parabolic equation h(t) + h(xxxx) + partial derivative(xx)|h(x)|(alpha) = f. It is shown that when 5/3 <= alpha < 7/3, the 3 alpha-5/alpha-1-dimensional parabolic Hausdorff measure of S is zero, which generalizes the recent corresponding work of Oz & aacute;nski and Robinson in [SIAM J. Math. Anal., 51, 228-255 (2019)] for alpha = 2 and f = 0. The same result is valid for a 3D modified Navier-Stokes system.

引用

页码：2219 / 2246

页数：28

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