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Acta Mathematica Scientia

, Volume 39, Issue 2, pp 420–428 | Cite as

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

  • Shanshan Guo
  • Zhong TanEmail author
Article

Abstract

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
$$\mathbb{S} = - P\left( \varrho \right) + 2\mu _0 \left( {1 + \left| {\mathbb{D}^d \left( u \right)} \right|^2 } \right)^{\left( {p - 2} \right)/2} \mathbb{D}^d \left( u \right) + \frac{{cdivu}}{{\left( {1 - c^a \left| {divu} \right|^a } \right)^{1/a} }}II.$$
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 ϱ is square integrable up to the boundary.

Key words

compressible fluid weak solutions non-Newtonian fluids integrability 

2010 MR Subject Classification

35Q35 35D30 76A05 76N99 

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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesXiamen UniversityXiamenChina
  2. 2.School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific ComputingXiamen UniversityXiamenChina

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