We are concerned with a system of nonlinear partial differential equations with p(x)-structure, 1 < p(infinity) <= p(x) <= p(0) < +infinity, and no-slip boundary conditions. We prove the existence and uniqueness of a C-1,C-gamma ((Omega) over bar) boolean AND W-2,W-2 (Omega) solution corresponding to small data, without further restrictions on the bounds p(infinity), p(0). In particular this result is applicable to the steady motion of shear-dependent electro-rheological fluids.
On the C^{1,\gamma}(\overline\Omega)\cap W^{2,2}(\Omega) regularity for a class of electro-rheological fluids
GRISANTI, CARLO ROMANO
2009-01-01
Abstract
We are concerned with a system of nonlinear partial differential equations with p(x)-structure, 1 < p(infinity) <= p(x) <= p(0) < +infinity, and no-slip boundary conditions. We prove the existence and uniqueness of a C-1,C-gamma ((Omega) over bar) boolean AND W-2,W-2 (Omega) solution corresponding to small data, without further restrictions on the bounds p(infinity), p(0). In particular this result is applicable to the steady motion of shear-dependent electro-rheological fluids.File in questo prodotto:
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