partial differential equations

A recurring task in the physical and data sciences is the rapid evaluation of sums of the form (1)

$$u_i = \sum_{j=1}^N G(x_i - y_j) q_j, \quad i=1,2,\ldots,N,$$

I joined the UC Davis Department of Mathematics in July 2025 as an Assistant Professor. My research focuses on fluid dynamics and partial differential equations, combining both analysis and computational approaches. Previously, I was a Visiting Assistant Professor at the University of California Berkeley. I received my Ph.D. in Applied Mathematics from the University of California Santa Cruz in 2023.

Imagine a boulder in a stream. As the water hits the boulder, it splits around the object. Once it’s passed around, the two flowing streams crash together, creating turbulent conditions that, if visible, would manifest as chaotic whorls and vortexes. This isn’t just true of water. It’s true of all fluids, including air. 

The mathematical equations underlying fluid motion — known as the Navier-Stokes equations — are among the most notoriously challenging partial differential equations because in principle they encode complex behaviors similar to the one you just imagined.

Isaac Neal received his Ph.D. from the Courant Institute at NYU in 2024. He studies partial differential equations with a focus on fluid dynamics. In particular, his research has delved into the formation of shocks in compressible fluids.
 

We are sad to report the passing of Professor Emeritus Allan Leonard Edelson on May 25, 2014 due to complications relating to Alzheimer's.