On control of shear flow of an upper convected Maxwell fluid

We consider parallel shear flow of an upper convected Maxwell fluid. A control is available in the form of a body force. The system of equations governing the velocity and shear stress is equivalent to a damped linear wave equation, and well known results imply that it is controllable if the time interval is sufficiently long for waves to propagate back and forth across the uncontrolled region. On the other hand, the issue of controlling normal stresses is far more difficult. If the control is available in the entire flow region, then normal stresses can be controlled, subject to a necessary positive definiteness constraint. On the other hand, if the control is confined to a subinterval, then the normal stresses are not controllable. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA,Weinheim.