Stokes problem with the possibility of controlling the velocity in a L-shaped domain

Abstract

The movement is studied from a viscous andincompressible homogeneous fluid which crosses a field of thechannel in the form of L, with the possibility to exert pressure ofknown difference between two opposite edges. We extend previous workin \cite{AB} which studies a problem of Stokes in the stationarycase and with one parameter that characterizes the pressuredifference between two sides in a specific domain (symmetricchannel). We show existence, unicity and regularity of the solutionof an evolution problem with four parameters that characterize thepressure difference between two opposite sides of our field.