de Araújo, G. M.; de Menezes, S. B. On a variational inequality for the Navier-Stokes operator with variable viscosity. (English) Zbl 1167.35432 Commun. Pure Appl. Anal. 5, No. 3, 583-596 (2006). Summary: We investigate the unilateral problem for the operator \(L\) perturbed of Navier-Stokes operator in a cylindrical case, where\[ Lu=u'-(\nu_0+\nu_1\|u(t)\|^2)\Delta u+(u\nabla)u-f+\nabla p. \]The mixed problem for the operator \(L\) was proposed by J. L. Lions [Quelques méthodes de résolution des problèmes aux limites non linéaires. Paris: Dunod; Paris: Gauthier-Villars (1969; Zbl 0189.40603)]. Using an appropriate penalization, we obtain a variational inequality for the Navier-Stokes perturbed system. Cited in 1 Document MSC: 35Q30 Navier-Stokes equations 35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000) 35J20 Variational methods for second-order elliptic equations Keywords:Navier-Stokes equations; variable viscosity; variational inequality Citations:Zbl 0189.40603 PDFBibTeX XMLCite \textit{G. M. de Araújo} and \textit{S. B. de Menezes}, Commun. Pure Appl. Anal. 5, No. 3, 583--596 (2006; Zbl 1167.35432) Full Text: DOI