6 papers
Incompressible Euler Blowup at the Threshold
Steve Shkoller
We prove finite-time Type--I blowup for the three-dimensional incompressible Euler equations in the axisymmetric no-swirl class, with initial velocity in $C^{1,α}(\mathbb{R}^3)\ca…
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…
Smooth and stable Euler implosions
Jiajie Chen, Steve Shkoller, Vlad Vicol
We construct a new class of self-similar implosion profiles for the multi-dimensional compressible Euler equations. These profiles are smooth, genuinely non-isentropic, radially/sp…
Intermittent Sub-grid Wave Correction from Differentiated Riemann Variables
Steve Shkoller
We introduce a low-cost every--step correction for one-dimensional Euler computations. The correction uses differentiated Riemann variables (DRVs) -- characteristic derivatives…
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--f…
Gradient catastrophes and an infinite hierarchy of Hölder cusp-singularities for 1D Euler
Isaac Neal, Steve Shkoller, Vlad Vicol
We establish an infinite hierarchy of finite-time gradient catastrophes for smooth solutions of the 1D Euler equations of gas dynamics with non-constant entropy. Specifically, for…