de Oliveira, H. B.2020-07-242020-07-242019-110219-5305http://hdl.handle.net/10400.1/14201The 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.engWeak solutionsExistenceRegularityFluidsNonlinear anisotropic viscosityGeneralized Navier-Stokesjournal article10.1142/S021953051950009X