On periodic Stokesian Hele-Shaw flows with surface tension. (English) Zbl 1148.76020
Summary: We consider a 2\(\pi \)-periodic and two-dimensional Hele-Shaw flow describing the motion of a viscous incompressible fluid. The free surface is moving under the influence of surface tension and gravity. The motion of the fluid is modelled using a modified version of Darcy’s law for Stokesian fluids. The bottom of the cell is assumed to be impermeable. We prove the existence of a unique classical solution for a domain which is a small perturbation of a cylinder. Moreover, we identify the equilibria of the flow and study their stability.
MSC:
| 76D25 | Wakes and jets |
| 76D45 | Capillarity (surface tension) for incompressible viscous fluids |
| 35Q35 | PDEs in connection with fluid mechanics |
References:
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