38 citations · 72 across the 20 of their papers we have counts for
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The geometry of maximal development and shock formation for the Euler equations in multiple space dimensions
Steve Shkoller, Vlad Vicol
We construct a fundamental piece of the boundary of the maximal globally hyperbolic development (MGHD) of Cauchy data for the multi-dimensional compressible Euler equations, which…
Anomalous diffusion by fractal homogenization
Scott Armstrong, Vlad Vicol
For every , we construct an explicit divergence-free vector field which is periodic in space and time and belongs to su…
A new type of stable shock formation in gas dynamics
Isaac Neal, Calum Rickard, Steve Shkoller +1
From an open set of initial data, we construct a family of classical solutions to the 1D nonisentropic compressible Euler equations which form cusps as a first singularit…
A characteristics approach to shock formation in 2D Euler with azimuthal symmetry and entropy
Isaac Neal, Steve Shkoller, Vlad Vicol
We provide a detailed analysis of the shock formation process for the non-isentropic 2d Euler equations in azimuthal symmetry. We prove that from an open set of smooth and generic…