The Taylor-Couette Problem for Flow in a Deformable Cylinder

The classical Taylor-Couette problem concerns the motion of a viscous incompressible fluid in the region between two rigid coaxial cylinders, which rotate at constant angular velocities. This is a fundamental example in bifurcation theory and hydrodynamic stability, and has been the subject of over 1500 papers. This lecture treats a generalization of this problem in which the outer cylinder is a deformable (nonlinearly viscoelastic) shell. Dynamical problems for the interaction of fluids with deformable solids undergoing large displacements are notoriously difficult to analyse. This is a rare instance of such an interaction in which the geometry is simple, the physics is interesting, and the behaviour of solutions can be determined by mathematical analysis, without an immediate recourse to numerical computation.