On non-Newtonian p-fluids. The pseudo-plastic case |
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Authors: | H. Beirã o da Veiga |
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Affiliation: | Dipartimento di Matematica Applicata U. Dini, via Buonarroti 1, I-56127 Pisa, PI, Italy |
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Abstract: | In the following we study a class of stationary Navier-Stokes equations with shear dependent viscosity, under the non-slip (Dirichlet) boundary condition. We consider pseudo-plastic fluids. A fluid is said pseudo-plastic, or shear thinning, if in Eq. (1.1) below one has p<2. We are interested in global (i.e., up to the boundary) regularity results, in dimension n=3, for the second order derivatives of the velocity and the first order derivatives of the pressure. We consider a cubic domain Ω and impose the non-slip boundary condition only on two opposite faces. On the other faces we assume periodicity, as a device to avoid effective boundary conditions. This choice is made so that we work in a bounded domain Ω and simultaneously with a flat boundary. |
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Keywords: | Navier-Stokes equations Non-Newtonian fluids Boundary value problems Regularity of solutions |
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