4 papers
Nonlinear stability of the Guderley imploding shock wave in radial symmetry
Giorgio Cialdea
We prove nonlinear stability of the Guderley imploding shock under radial perturbations for the three-dimensional compressible Euler equations in the adiabatic range $1<γ\leq\frac{…
A new class of Euler explosions
Jiajie Chen, Giorgio Cialdea, Steve Shkoller +1
We study the global-in-time continuation, past the singularity, of the smooth, non-isentropic, radially symmetric imploding solutions of the compressible Euler equations recently c…
Classical Euler flows generate the strong Guderley imploding shock wave
Giorgio Cialdea, Steve Shkoller, Vlad Vicol
We prove that Guderley's self-similar imploding shock solution for the compressible Euler equations with ideal--gas law () arises from classical, radially symmetric, shock--fr…
Vorticity blowup in 2D compressible Euler equations
Jiajie Chen, Giorgio Cialdea, Steve Shkoller +1
We prove finite-time vorticity blowup for smooth solutions of the 2D compressible Euler equations with smooth, localized, and non-vacuous initial data. The vorticity blowup occurs…