Abstract
We consider here a $2\pi$-periodic and two-dimensional Hele–Shaw flow modelling the motion of a viscous and incompressible fluid. The free surface is moving under the influence of gravity and is modelled by a modified Darcy law for Stokesian fluids. The bottom of the cell is assumed to be impermeable. We prove the existence of a unique classical solution if the initial data is near a constant, identify the equilibria of the flow, and study their stability.
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