Vorticity, symmetries, ill-posedness and singularity formation in incompressible fluids
North Carolina State University
Abstract
Many fundamental fluid flows can be described succinctly in terms of fluid vorticity. However, often the vorticities associated with physical flows are not smooth: examples include shear layers, spirals, and vortices. Many mathematical challenges come as a consequence of non-smooth vorticities. In this talk, I’ll give an overview of some of these mathematical questions. In particular, I’ll describe recent mathematical work which utilizes symmetry solutions to better understand two-dimensional incompressible flows: these works describe fundamental ill-posedness of flows with singular vorticities, as well as a universal tendency for Lagrangian representations to become less smooth over time. This talk will aim to be accessible to a broad audience interested in fluid dynamics. This represents joint work with Alberto Bressan, Galen Wilcox, Ayman Rimah, and Tarek Elgindi.
About the speaker
Dr. Ryan Murray is an Assistant Professor in the Department of Mathematics at North Carolina State University. Previously, he was a Chowla Assistant Research Professor in the Department of Mathematics at Penn State University (2016–2019), and he earned his Ph.D. at Carnegie Mellon (2016). Ryan’s work focuses on using tools from mathematical analysis to understand a wide range of applied problems, including problems from fluid dynamics and data science.
