Multidimensional Hele‐Shaw flows modelling Stokesian fluids
Joachim Escher, Bogdan–Vasile Matioc · Mathematical Methods in the Applied Sciences · 2008
Abstract We consider here an n‐dimensional periodic flow describing the motion of an incompressible Stokesian fluid in a Hele‐Shaw cell. The free surface separating the fluid from air, at pressure normalized to be zero, is moving under the influence of gravity and surface tension. We prove the existence of a unique classical Hölder solution for small perturbations of cylinders. Moreover, we evidence the existence of a single steady state and prove its exponential stability. Copyright © 2008 John Wiley & Sons, Ltd.