ON MAXIMUM MODULUS ESTIMATES OF THE NAVIER-STOKES EQUATIONS WITH NONZERO BOUNDARY DATA

被引：2

作者：

Chang, Tongkeun ^{[1
]}

Choe, Hi Jun ^{[1
]}

Kang, Kyungkeun ^{[1
]}

机构：

[1] Yonsei Univ, Dept Math, 50 Yonsei Ro, Seoul 120749, South Korea

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2018年 / 50卷 / 03期

关键词：

Navier-Stokes equations; maximum modulus principle; very weak solutions; SPACES;

D O I：

10.1137/17M1152565

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider discontinuous influx for the Navier-Stokes flow and construct a solution that is unbounded in a neighborhood of a discontinuous point of given bounded boundary data for any dimension larger than or equal to two. This is an extension of the result in [T. Chang and H. Choe, J. Differential Equations, 254 (2013), pp. 2682-2704] that a blow-up solution exists with a bounded and discontinuous boundary data for the Stokes flow. If the normal component of bounded boundary data is Dini-continuous in space or log-Dini-continuous in time, then the constructed solution becomes bounded and a maximum modulus estimate is valid.

引用

页码：3147 / 3171

页数：25

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