On Integrability Up to the Boundary of the Weak Solutions to a Non-Newtonian Fluid

被引：2

作者：

Guo, Shanshan ^{[1
]}

Tan, Zhong ^{[1
,2
]}

机构：

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

[2] Xiamen Univ, Fujian Prov Key Lab Math Modeling & Sci Comp, Xiamen 361005, Fujian, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2019年 / 39卷 / 02期

基金：

中国国家自然科学基金;

关键词：

compressible fluid; weak solutions; non-Newtonian fluids; integrability; NAVIER-STOKES EQUATIONS; EXISTENCE; FLOWS;

D O I：

10.1007/s10473-019-0208-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This work consider boundary integrability of the weak solutions of a non-Newtonian compressible fluids in a bounded domain in dimension three, which has the constitutive equations as S=-P(rho)+2 mu(0)(1+vertical bar D-d(u)vertical bar(2))D-(p-2)/2(d)(u)+cdivu/(1-c(a)vertical bar divu vertical bar(a))(1/a) The existence result of weak solutions can be get based on Galerkin approximation. With the linear operator B constructed by BOGOVSKII, we show that the density ? is square integrable up to the boundary.

引用

页码：420 / 428

页数：9

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