Analysis Seminar

Simultaneous development of shocks and cusps for 2D compressible Euler from smooth initial data

Speaker: Steve Shkoller, UC Davis

Location: Online Online

Date: Thursday, April 29, 2021, 11 a.m.


A fundamental question in fluid dynamics concerns the formation of discontinuous shock waves from smooth initial data. In previous works, we have established stable generic shock formation for the compressible Euler system, showing that at the first singularity the solution has precisely C1/3 Holder regularity, a so-called preshock. The focus of this talk is a complete space-time description of the solution after this initial singularity. We show that three surfaces of discontinuity emerge simultaneously and instantaneously from the preshock: the classical shock discontinuity that propagates by the Rankine–Hugoniot conditions, together with two distinct surfaces in space-time, along which C3/2 cusp singularities form.