| Abstract: |
| The Hele-Shaw flow is a model for the evolution of an ideal fluid occupying the narrow gap between two parallel plates and subject to an external pressure source. Assuming the fluid interface is given by the graph of a function, it can be shown that this function must solve a parabolic integro-differential equation of 1st order. I will discuss recent joint work with Russell Schwab (Michigan State University) on the regularization properties of such nonlocal parabolic equations. Our results allow us, in certain model scenarios and for short enough times, to conclude improvement-of-regularity for the fluid interface. |
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