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

共 45 条

[31] A sufficient integral condition for local regularity of solutions to the surface growth model [J].

Ozanski, Wojciech S. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2019, 276 (10) :2990-3013

[32] PARTIAL REGULARITY FOR A SURFACE GROWTH MODEL [J].

Ozanski, Wojciech S. ;

Robinson, James C. .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2019, 51 (01) :228-255

[33] Partial regularity of suitable weak solutions to the multi-dimensional generalized magnetohydrodynamics equations [J].

Ren, Wei ;

Wang, Yanqing ;

Wu, Gang .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2016, 18 (06)

[34]

Scheven C, 2011, REV MAT IBEROAM, V27, P751

[35] Amorphous molecular beam epitaxy: global solutions and absorbing sets [J].

Stein, O ;

Winkler, M .

EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2005, 16 :767-798

[36] ON THE HOLDER CONTINUITY OF BOUNDED WEAK SOLUTIONS OF QUASILINEAR PARABOLIC-SYSTEMS [J].

STRUWE, M .

MANUSCRIPTA MATHEMATICA, 1981, 35 (1-2) :125-145

[37] DYNAMICS OF DRIVEN INTERFACES WITH A CONSERVATION LAW [J].

SUN, T ;

GUO, H ;

GRANT, M .

PHYSICAL REVIEW A, 1989, 40 (11) :6763-6766

[38] SURFACE-DIFFUSION-DRIVEN KINETIC GROWTH ON ONE-DIMENSIONAL SUBSTRATES [J].

TAMBORENEA, PI ;

DASSARMA, S .

PHYSICAL REVIEW E, 1993, 48 (04) :2575-2594

[39] Partial Regularity of Suitable Weak Solutions to the Fractional Navier-Stokes Equations [J].

Tang, Lan ;

Yu, Yong .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2015, 334 (03) :1455-1482

[40] A new proof of partial regularity of solutions to Navier-Stokes equations [J].

Vasseur, Alexis F. .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2007, 14 (5-6) :753-785

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