Analysis, Dynamics and Applications Seminar

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 satisfy a nonlinear 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 equations. Our results allow us, in certain model scenarios and for short enough times, to establish an improvement-of-regularity phenomenon for the fluid interface.

Place: Hybrid, Math, 402 and Zoom: https://arizona.zoom.us/j/81150211038  Password: “arizona” (all lower case)