Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45367320210701On Integrability up to the Boundary of the Weak Solutions to a Class of non-Newtonian Compressible Fluids with Vacuum152715361658210.22055/jacm.2021.35444.2655ENJanMuhammadSchool of Mathematics, Department of Mathematics, CNS, Northwest University, Xi’an, 710127, P. R. China0000-0001-8872-2523AbdulSamadSchool of Mathematics, Department of Mathematics, Northwest University, Xi’an, 710127, P. R. China0000-0002-0887-9860Journal Article20201015In 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 ℝ<sup>3</sup> 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.https://jacm.scu.ac.ir/article_16582_235256edd1c082ccb7a6417ed5686664.pdf