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math.AP2025
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…
math.AP2025
Anomalous diffusion via iterative quantitative homogenization: an overview of the main ideas
Scott Armstrong, Vlad Vicol
Anomalous diffusion is the fundamental ansatz of phenomenological theories of passive scalar turbulence, and has been confirmed numerically and experimentally to an extraordinary e…
math.AP2025
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…