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

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## 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
The existence result of weak solutions can be get based on Galerkin approximation. With the linear operator

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

*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## Preview

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