Nonstationary Stokes System with Variable Viscosity in Bounded and Unbounded Domains

摘要: We consider a generalization of the nonstationary Stokes system, where the constant viscosity is replaced by general given positive function. Such system arises in many situations as linearized when of an incompressible, viscous fluid depends on some other quantities. prove unique solvability system with optimal regularity $L^q$-Sobolev spaces, particular for exterior force $f\in L^q(Q_T)$. Moreover, we characterize domains fractional powers associated operators $A_q$ and obtain corresponding result L^q(0,T;\mathcal{D}(A_q^\alpha))$. The holds class including bounded domain, domains, aperture infinite cylinder asymptotically flat layer $W^{2-\frac1r}_r$-boundary $r>d$ $r\geq \max(q,q')$.