INTERIOR ESTIMATES FOR POWER-LAW SHEAR-THICKENING FLUIDS
In this paper, we establish interior estimates for the symmetric gradient of local weak solutions to equation
where and is a domain.
power law fluids, shear thickening fluids, estimates.
Received: February 17, 2021; Accepted: March 3, 2021; Published: March 19, 2021
How to cite this article: Gilberlandio J. Dias, Interior Estimates for Power-Law Shear-Thickening Fluids, Advances and Applications in Fluid Mechanics 26(1) (2021), 49-66. DOI: 10.17654/FM026010049
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] J. W. Barrett and W. B. Liu, Finite element approximation of the p-Laplacian, Math. Comp. 61(204) (1993), 523-537.[2] T. Bhattacharya, E. DiBenedetto and J. Manfredi, Limits as of and related extremal problems, Sem. Mat. Univ. Pol. Torino. Fascicolo Speciale, Nonlinear PDE’s (1989), 15-68.[3] G. J. Dias, Stationary Problems for Incompressible Fluids with a Power Law in Channels with Unlimited domains, Tesis PhD, Universidade Estadual de Campinas - UNICAMP, 2011.[4] L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, Vol. 19, American Mathematical Society, Providence, RI, 1998.[5] G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems, 2nd ed., Springer-Verlag, Berlin, 2011.[6] P. Tolksdorf, Everywhere regularity for some quasilinear systems with a lack of ellipticity, Ann. Mat. Pura Appl. 134 (1983), 241-266.[7] K. Uhlenbeck, Regularity for a class of nonlinear elliptic systems, Acta. Math. 138 (1977), 219-240.