Jan Muhammad - School of Mathematics, Department of Mathematics, CNS, Northwest University, Xi’an, ۷۱۰۱۲۷, P. R. China
Abdul Samad - School of Mathematics, Department of Mathematics, Northwest University, Xi’an, ۷۱۰۱۲۷, P. R. China

In this paper, we study the integrability up to the boundary of the weak solutions of non-Newtonian compressible fluid with a nonlinear constitutive equation in ℝ۳ bounded domain. Galerkin approximation will be used for existence of weak solutions and by applying the bounded linear operator B, introduced by Bogovskii, we prove the square integrability of the density up to the boundary.

Compressible non-Newtonian fluid, weak solutions, vacuum, integrability