Abstract
The Muskat problem models the motion of two immiscible fluids in a porous medium. We assume that the medium occupies the exterior of a circle r= δ, that the fluids are incompressible, and that the capillary pressure at the interface is nonnegligible. We take any radially symmetric stationary solution with interface r= R s , R s > δ, and consider the Muskat problem for an initial interface r= R s + ελ 0( θ), | ε| small. We prove that this problem has a unique global solution which is analytic in ε and which converges to the stationary solution, provided λ 0 satisfies a sequence of nonlinear constraints. These constraints are satisfied in the case where λ 0(θ)=∑ |m|<∞λ m e imlθ , l any integer ⩾2. The nonlinear constraints are, under some assumptions on the solution, also necessary.
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