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\(C^{1,\alpha}\)-regularity for electrorheological fluids in two dimensions. (English) Zbl 1132.76301

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 \(\inf p > \frac{6}{5}\).

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
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