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Existence results in interfacial flows with kinetic undercooling regularization in a time-dependent gap Hele-Shaw cell

Presented by: 
Xie Xuming
Friday 1st November 2019 - 16:00 to 17:00
INI Seminar Room 1

Hele-Shaw cells where the top plate is lifted uniformly at a prescribed speed and the bottom plate is fixed have been used to study interface related problems. Our talk focuses on an interface flow with kinetic undercooling regularization in a radial Hele-Shaw cell with a time dependent gap. We obtain the local existence of analytic solution of the moving boundary problem when the initial data is analytic. The methodology is to use complex analysis and reduce the free boundary problem to a Riemann-Hilbert problem and an abstract Cauchy-Kovalevsky evolution problem. A similar free boundary problem in multidimensional spaces is also studied and the local existence of classical solutions can be obtained.

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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons