Tue, April 7, 2026
2:30 pm - 3:30 pm
Journalism Building JR0353
Cole Graham
University of Wisconsin-Madison
Title
Vanishing viscosity and shock formation in 1D conservation laws
Abstract
Like many conservation laws, the compressible Euler equations readily form shocks from smooth data. However, their viscous counterparts like Navier–Stokes typically prevent such singularities. This talk will focus on the interface between these behaviors: the vanishing-viscosity limit near shock formation. Using a matched asymptotic expansion to bridge hyperbolic and parabolic dynamics, we identify the sharp vanishing-viscosity rate in Hölder norms and uncover a universal viscous layer near shock formation. This is joint work with John Anderson and Sanchit Chaturvedi.