Large-time asymptotics of Stokes flow for perturbed balls with injection and suction

We discuss large-time behaviour of Stokes flow with surface tension and with injection or suction in one point. We consider domains in R or R that are initially small perturbations of balls. After a suitable time-dependent rescaling, a ball becomes a stationary solution. To prove stability of this solution, we derive a nonlinear non-local evolution equation describing the motion of perturbed domains. From spectral properties of the linearisation, we find global existence in time and decay properties for the injection case. For the suction case, we find that an arbitrarily large portion of liquid smaller than the entire domain can be removed if the initial domain is close enough to a ball. AMS subject classifications: 35R35, 35K55, 76D07