##### Department of Mathematics,

University of California San Diego

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### MATH 248 Seminar In Real Analysis

## Prof. Yuming Paul Zhang

#### Auburn U

## Regularity of Hele-Shaw flow with source and drift: Flat free boundaries are Lipschitz

##### Abstract:

The classical Hele-Shaw flow describes the motion of incompressible viscous fluid, which occupies part of the space between two parallel, nearby plates. With source and drift, the equation is used in models of tumor growth where cells evolve with contact inhibition, and congested population dynamics. We consider the flow with Hölder continuous source and Lipschitz continuous drift. We show that if the free boundary of the solution is locally close to a Lipschitz graph, then it is indeed Lipschitz, given that the Lipschitz constant is small. This is joint work with Inwon Kim.

Host: Prof. Andrej Zlatos

### May 30, 2023

### 11:00 AM

APM 7321

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