Shock formation in weakly viscous conservation laws

Series
PDE Seminar
Time
Friday, October 4, 2024 - 2:00pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Cole Graham – University of Wisconsin–Madison – graham@math.wisc.eduhttps://colegraham.net/
Organizer
Leonardo Abbrescia

The compressible Euler equations readily form shocks, but in 1D the inclusion of viscosity prevents such singularities. In this talk, we will quantitatively examine the interaction between generic shock formation and viscous effects as the viscosity tends to zero. We thereby obtain sharp rates for the vanishing-viscosity limit in Hölder norms, and uncover universal viscous structure near shock formation. The results hold for large classes of viscous hyperbolic conservation laws, including compressible Navier–Stokes with physical rather than artificial viscosity. This is joint work with John Anderson and Sanchit Chaturvedi.