[1] Abbatiello, A., Bulíček, M., Kaplický, P.: On the existence of classical solution to the steady flows of generalized Newtonian fluid with concentration dependent power-law index. J. Math. Fluid Mech. 21 (2019), Article ID 15, 22 pages. DOI 10.1007/s00021-019-0415-8 | MR 3911730 | Zbl 1414.35160

[2] Acerbi, E., Mingione, G.: Regularity results for stationary electro-rheological fluids. Arch. Ration. Mech. Anal. 164 (2002), 213-259. DOI 10.1007/s00205-002-0208-7 | MR 1930392 | Zbl 1038.76058

[3] Acerbi, E., Mingione, G.: Gradient estimates for the $p(x)$-Laplacian system. J. Reine Angew. Math. 584 (2005), 117-148. DOI 10.1515/crll.2005.2005.584.117 | MR 2155087 | Zbl 1093.76003

[4] Antontsev, S. N., Rodrigues, J. F.: On stationary thermo-rheological viscous flows. Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 52 (2006), 19-36. DOI 10.1007/s11565-006-0002-9 | MR 2246902 | Zbl 1117.76004

[5] Veiga, H. Beirão da, Kaplický, P., Růžička, M.: Boundary regularity of shear thickening flows. J. Math. Fluid Mech. 13 (2011), 387-404. DOI 10.1007/s00021-010-0025-y | MR 2824490 | Zbl 1270.35360

[6] Bennett, C., Sharpley, R.: Interpolation of Operators. Pure and Applied Mathematics 129. Academic Press, Boston (1988). MR 0928802 | Zbl 0647.46057

[7] Berselli, L. C., Diening, L., Růžička, M.: Existence of strong solutions for incompressible fluids with shear dependent viscosities. J. Math. Fluid Mech. 12 (2010), 101-132. DOI 10.1007/s00021-008-0277-y | MR 2602916 | Zbl 1261.35118

[8] Breit, D., Mensah, P. R.: Space-time approximation of parabolic systems with variable growth. IMA J. Numer. Anal. 40 (2020), 2505-2552. DOI 10.1093/imanum/drz039 | MR 4167054 | Zbl 1466.65122

[9] Bulíček, M., Ettwein, F., Kaplický, P., Pražák, D.: The dimension of the attractor for the 3D flow of a non-Newtonian fluid. Commun. Pure Appl. Anal. 8 (2009), 1503-1520. DOI 10.3934/cpaa.2009.8.1503 | MR 2505283 | Zbl 1200.37074

[10] Bulíček, M., Ettwein, F., Kaplický, P., Pražák, D.: On uniqueness and time regularity of flows of power-law like non-Newtonian fluids. Math. Methods Appl. Sci. 33 (2010), 1995-2010. DOI 10.1002/mma.1314 | MR 2744616 | Zbl 1202.35152

[11] Bulíček, M., Kaplický, P., Pražák, D.: Uniqueness and regularity of flows of non-Newtonian fluids with critical power-law growth. Math. Models Methods Appl. Sci. 29 (2019), 1207-1225. DOI 10.1142/S0218202519500209 | MR 3963639 | Zbl 1425.35147

[12] Bulíček, M., Pustějovská, P.: On existence analysis of steady flows of generalized Newtonian fluids with concentration dependent power-law index. J. Math. Anal. Appl. 402 (2013), 157-166. DOI 10.1016/j.jmaa.2012.12.066 | MR 3023245 | Zbl 1308.76068

[13] Bulíček, M., Pustějovská, P.: Existence analysis for a model describing flows of an incompressible chemically reacting non-Newtonian fluid. SIAM J. Math. Anal. 46 (2014), 3223-3240. DOI 10.1137/130927589 | MR 3262601 | Zbl 1308.35199

[14] Burczak, J., Kaplický, P.: Evolutionary, symmetric $p$-Laplacian. Interior regularity of time derivatives and its consequences. Commun. Pure Appl. Anal. 15 (2016), 2401-2445. DOI 10.3934/cpaa.2016042 | MR 3565947 | Zbl 1362.35160

[15] Crispo, F.: A note on the existence and uniqueness of time-periodic electro-rheological flows. Acta Appl. Math. 132 (2014), 237-250. DOI 10.1007/s10440-014-9897-9 | MR 3255040 | Zbl 1295.76004

[16] Diening, L.: Theoretical and Numerical Results for Electrorheological Fluids: Ph. D. Thesis. Universität Freiburg, Freiburg im Breisgau (2002). Zbl 1022.76001

[17] Diening, L., Růžička, M.: Strong solutions for generalized Newtonian fluids. J. Math. Fluid Mech. 7 (2005), 413-450. DOI 10.1007/s00021-004-0124-8 | MR 2166983 | Zbl 1080.76005

[18] Diening, L., Růžička, M., Wolf, J.: Existence of weak solutions for unsteady motion of generalized Newtonian fluids. Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 9 (2010), 1-46. DOI 10.2422/2036-2145.2010.1.01 | MR 2668872 | Zbl 1253.76017

[19] Evans, L. C.: Partial Differential Equations. Graduate Studies in Mathematics 19. AMS, Providence (1998). DOI 10.1090/gsm/019 | MR 1625845 | Zbl 0902.35002

[20] Frehse, J., Schwarzacher, S.: On regularity of the time derivative for degenerate parabolic systems. SIAM J. Math. Anal. 45 (2015), 3917-3943. DOI 10.1137/141000725 | MR 3411724 | Zbl 1325.35108

[21] Frigeri, S., Grasselli, M., Pražák, D.: Nonlocal Cahn-Hilliard-Navier-Stokes systems with shear dependent viscosity. J. Math. Anal. Appl. 459 (2018), 753-777. DOI 10.1016/j.jmaa.2017.10.078 | MR 3732553 | Zbl 1382.35218

[22] Grasselli, M., Pražák, D.: Regularity results for a Cahn-Hilliard-Navier-Stokes system with shear dependent viscosity. Z. Anal. Anwend. 33 (2014), 271-288. DOI 10.4171/ZAA/1511 | MR 3229587 | Zbl 1297.35185

[23] Kaplický, P.: Time regularity of flows of non-Newtonian fluids. IASME Trans. 2 (2005), 1232-1236. MR 2214014

[24] Ladyzhenskaya, O. A.: The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach, New York (1969). MR 0254401 | Zbl 0184.52603

[25] Málek, J., Nečas, J., Rokyta, M., Růžička, M.: Weak and Measure-Valued Solutions to Evolutionary PDEs. Applied Mathematics and Mathematical Computation 13. Chapman & Hall, London (1996). DOI 10.1201/9780367810771 | MR 1409366 | Zbl 0851.35002

[26] Málek, J., Nečas, J., Růžička, M.: On weak solutions to a class of non-Newtonian incompressible fluids in bounded three-dimensional domains: The case $p\geq 2$. Adv. Differ. Equ. 6 (2001), 257-302. DOI 10.57262/ade/1357141212 | MR 1799487 | Zbl 1021.35085

[27] Naumann, J., Wolf, J., Wolff, M.: On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions. Commentat. Math. Univ. Carol. 39 (1998), 237-255. MR 1651938 | Zbl 0940.35046

[28] Pastukhova, S. E.: Nonstationary version of Zhikov's compensated compactness lemma and its application to the solvability of the generalized Navier-Stokes equations. Dokl. Math. 81 (2010), 66-71. DOI 10.1134/S1064562410010199 | MR 2675418 | Zbl 1202.35161

[29] Růžička, M.: Electrorheological Fluid: Modeling and Mathematical Theory. Lecture Notes in Mathematics 1748. Springer, Berlin (2000). DOI 10.1007/BFb0104029 | MR 1810360 | Zbl 0962.76001

[30] Růžička, M.: Modeling, mathematical and numerical analysis of electrorheological fluids. Appl. Math., Praha 49 (2004), 565-609. DOI 10.1007/s10492-004-6432-8 | MR 2099981 | Zbl 1099.35103

[31] Simon, J.: Sobolev, Besov and Nikolskii fractional spaces: Imbeddings and comparisons for vector valued spaces on an interval. Ann. Mat. Pura Appl., IV. Ser. 157 (1990), 117-148. DOI 10.1007/BF01765315 | MR 1108473 | Zbl 0727.46018

[32] Sin, C.: The existence of strong solutions to steady motion of electrorheological fluids in 3D cubic domain. J. Math. Anal. Appl. 445 (2017), 1025-1046. DOI 10.1016/j.jmaa.2016.07.019 | MR 3543809 | Zbl 1352.35124

[33] Sin, C.: The existence of weak solutions for steady flows of electrorheological fluids with nonhomogeneous Dirichlet boundary condition. Nonlinear Anal., Theory Methods Appl., Ser. A 163 (2017), 146-162. DOI 10.1016/j.na.2017.06.014 | MR 3695973 | Zbl 1375.35400

[34] Sin, C.: Boundary partial $C^{1,\alpha}$-regularity for stationary shear thickening flows in 3D. J. Math. Fluid Mech. 20 (2018), 1617-1639. DOI 10.1007/s00021-018-0379-0 | MR 3877488 | Zbl 1404.35080

[35] Sin, C.: Global regularity of weak solutions for steady motions of electrorheological fluids in 3D smooth domain. J. Math. Anal. Appl. 461 (2018), 752-776. DOI 10.1016/j.jmaa.2017.10.081 | MR 3759566 | Zbl 1387.35082

[36] Sin, C.: Boundary partial regularity for steady flows of electrorheological fluids in 3D bounded domains. Nonlinear Anal., Theory Methods Appl., Ser. A 179 (2019), 309-343. DOI 10.1016/j.na.2018.08.009 | MR 3886635 | Zbl 1404.35079

[37] Sin, C.: Local higher integrability for unsteady motion equations of generalized Newtonian fluids. Nonlinear Anal., Theory Methods Appl., Ser. A 200 (2020), Article ID 112029, 23 pages. DOI 10.1016/j.na.2020.112029 | MR 4111765 | Zbl 1450.35225

[38] Sin, C., Baranovskii, E. S.: Hölder continuity of solutions for unsteady generalized NavierStokes equations with $p(x,t)$-power law in 2D. J. Math. Anal. Appl. 517 (2023), Article ID 126632, 31 pages. DOI 10.1016/j.jmaa.2022.126632 | MR 4486161 | Zbl 1498.35438

[39] Sohr, H.: The Navier-Stokes Equations: An Elementary Functional Analytic Approach. Birkhäuser Advanced Texts. Birkhäuser, Basel (2001). DOI 10.1007/978-3-0348-8255-2 | MR 1928881 | Zbl 0983.35004

[40] Temam, R.: Navier-Stokes Equations: Theory and Numerical Analysis. Studies in Mathematics and its Applications 2. North-Holland, Amsterdam (1984). MR 0769654 | Zbl 0568.35002

[41] Zhikov, V. V.: New approach to the solvability of generalized Navier-Stokes equations. Funct. Anal. Appl. 43 (2009), 190-207. DOI 10.1007/s10688-009-0027-9 | MR 2583638 | Zbl 1271.35061