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PDEs & Applications Seminar

Friday, March 7, 2025

Time: 10:30 a.m.  Place: Jeffery Hall, Room 319

Speaker: Grigalius Taujanskas (University of Cambridge)

Title: Mathematical Theory of Carrollian Fluids in 1+1 Dimensions

Abstract: Due to connections to flat space holography, Carrollian geometry, physics and fluid dynamics have received an explosion of interest over the last two decades. In the "Carrollian limit" of vanishing speed of light c, relativistic fluids reduce to a set of PDEs called the Carrollian fluid equations. Although in general these equations are not well understood analytically, and their PDE theory does not appear to have been studied, in dimensions 1+1 it turns out that there is a duality with the Galilean compressible Euler equations in 1+1 dimensions inherited from the isomorphism of the Carrollian (c to 0) and Galilean (c to infinity) contractions of the Poincaré algebra. Under this duality time and space are interchanged, leading to different dynamics in evolution. I will discuss recent work with N. Athanasiou (Thessaloniki), M. Petropoulos (Paris) and S. Schulz (Pisa) in which we establish the first rigorous PDE results for these equations by introducing a notion of Carrollian isentropy and studying the equations using Lax’s method and compensated compactness. In particular, I will explain that there is global existence in rough norms but finite-time blow-up in smoother norms.