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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\u2013Stokes equations with (linear) anisotropic viscosity used to model either the turbulence or the Ekman layer in atmospheric and oceanic fluid flows.<\/jats:p>","DOI":"10.1142\/s021953051950009x","type":"journal-article","created":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T06:01:06Z","timestamp":1560492066000},"page":"977-1003","source":"Crossref","is-referenced-by-count":2,"title":["Generalized Navier\u2013Stokes equations with nonlinear anisotropic viscosity"],"prefix":"10.1142","volume":"17","author":[{"given":"H. 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