Leonardo Abbrescia

Vanderbilt University, April 5, 12:00 pm

The mathematics of shockwaves

Shockwaves are very prevalent in physical phenomena: supernova explosions, high-energy particle collisions, condensed matter under extreme conditions, etc. From these situations, one might intuitively think that there is some violent mechanism driving a shock. In this talk, we will see how the mathematics of shock waves proves that this is not the case. For the PDEs that model many of the physical systems we care about, shock waves can form in finite time even for small and completely smooth initial conditions. Moreover, the state variables are bounded at the initial shock singularity. Most of the talk will focus on Burgers’ equation and 1D compressible isentropic Euler, but we will discuss more recent work if time permits.