Generalized Navier-Stokes equations with nonlinear anisotropic viscosity

de Oliveira, H. B.

http://hdl.handle.net/10400.1/14201

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Authors

de Oliveira, H. B.

Abstract(s)

The purpose of this work is to study the generalized Navier-Stokes equations with nonlinear viscosity that, in addition, can be fully anisotropic. Existence of very weak solutions is proved for the associated initial and boundary-value problem, supplemented with no-slip boundary conditions. We show that our existence result is optimal in some directions provided there is some compensation in the remaining directions. A particular simplification of the problem studied here, reduces to the Navier-Stokes equations with (linear) anisotropic viscosity used to model either the turbulence or the Ekman layer in atmospheric and oceanic fluid flows.