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

作　　者：Yan Qing WANG Yi Ke HUANG Gang WU Dao Guo ZHOU 

机构地区：[1]College of Mathematics and Information Science,Zhengzhou University of Light Industry,Zhengzhou 450002,P.R.China [2]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,P.R.China [3]School of Mathematics,Hangzhou Normal University,Hangzhou 311121,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第11期2219-2246,共28页数学学报（英文版）

基　　金：the National Natural Science Foundation of China(Grant Nos.11971446,11601492,11771423 and12071113);Natural Science Foundation of He’nan(Grant No.232300421077);Research Start-up Funding Program of Hangzhou Normal University(Grant No.4235C50223204065)。

摘　　要：In this paper,we are concerned with the precise relationship between the Hausdorff dimension of possible singular point set S of suitable weak solutions and the parameterαin the nonlinear term in the following parabolic equationh_(t)+h_(xxxx)+∂_(xx)|h_(x)|^(α)=f.It is shown that when 5/3≤α<7/3,the 3α-5/α−1-dimensional parabolic Hausdorff measure of S is zero,which generalizes the recent corresponding work of Ozánski and Robinson in[SIAM J.Math.Anal.,51,228–255(2019)]forα=2 and f=0.The same result is valid for a 3D modified Navier–Stokes system.

关 键 词：Surface growth model modified Navier–Stokes equations partial regularity Hausdorff dimension 

分 类 号：O175[理学—数学]