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Title: Global existence and decay for solutions of the Hele-Shaw flow with injection


Speaker: Cheng, C. H. Arthur, National Central University, Taiwan


Abstract: We examine the stability and decay of the free boundary perturbations in a Hele-Shaw cell under the injection of fluid. In particular,we study the perturbations of spherical boundaries as time t \to \infty.In the presence of positive surface tension, we examine both slow and fast injection rates.When fluid is injected slowly, the perturbations decay back to an expanding sphere exponentially fast, while for fast injection, the perturbation decays to an expanding sphere with an algebraic rate. In the absence of surface tension, we study the case of a constant injection rate, and prove that perturbations of thesphere decay like (1+t)^{-0.5+\epsilon) for \epsilon > 0 small.


Time: 15:00-16:30, Friday, March 16.


Place: Lecture Room 1105, Mengminwei Building


邀请人:孙永忠 老师