Abels, Helmut Nonstationary Stokes system with variable viscosity in bounded and unbounded domains. (English) Zbl 1191.76038 Discrete Contin. Dyn. Syst., Ser. S 3, No. 2, 141-157 (2010). Summary: We consider a generalization of the nonstationary Stokes system, where the constant viscosity is replaced by a general given positive function. Such a system arises in many situations as linearized system, when the viscosity of an incompressible, viscous fluid depends on some other quantities. We prove unique solvability of the nonstationary system with optimal regularity in \(L^q\)-Sobolev spaces, in particular for an exterior force \(f \in L^q(Q_T)\). Moreover, we characterize the domains of fractional powers of some associated Stokes operators \(A_q\) and obtain a corresponding result for \(f \in L^q (0,T;\mathcal {D}(A_q^{\alpha}))\). The result holds for a general class of domains including bounded domain, exterior domains, aperture domains, infinite cylinder and asymptotically flat layer with \(W^{2- \frac1r}_r\)-boundary for some \(r>d\) with \(r\geq \max (q,q^{\prime})\). Cited in 15 Documents MSC: 76D07 Stokes and related (Oseen, etc.) flows 35Q30 Navier-Stokes equations 47F05 General theory of partial differential operators Keywords:Stokes equation; Stokes operator; unbounded domains; maximal regularity; domains of fractional powers PDFBibTeX XMLCite \textit{H. Abels}, Discrete Contin. Dyn. Syst., Ser. S 3, No. 2, 141--157 (2010; Zbl 1191.76038) Full Text: DOI