Diening, L.; Ettwein, F.; Růžička, M. \(C^{1,\alpha}\)-regularity for electrorheological fluids in two dimensions. (English) Zbl 1132.76301 NoDEA, Nonlinear Differ. Equ. Appl. 14, No. 1-2, 207-217 (2007). Summary: We prove the existence of \(C^{1,\alpha}_{\mathrm{loc}}\)-solutions to a system of nonlinear partial differential equations describing steady planar motions of electrorheological fluids with Dirichlet boundary conditions for \(\inf p > \frac{6}{5}\). Cited in 28 Documents MSC: 76A05 Non-Newtonian fluids 35B65 Smoothness and regularity of solutions to PDEs 35Q35 PDEs in connection with fluid mechanics 35J60 Nonlinear elliptic equations 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 76W05 Magnetohydrodynamics and electrohydrodynamics PDFBibTeX XMLCite \textit{L. Diening} et al., NoDEA, Nonlinear Differ. Equ. Appl. 14, No. 1--2, 207--217 (2007; Zbl 1132.76301) Full Text: DOI