576 citations · 1.5k across the 43 of their papers we have counts for
51 papers
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…
A fast dynamic smooth adaptive meshing scheme with applications to compressible flow
Raaghav Ramani, Steve Shkoller
We develop a fast-running smooth adaptive meshing (SAM) algorithm for dynamic curvilinear mesh generation, which is based on a fast solution strategy of the time-dependent Monge-Am…
3D Interface Models for Rayleigh-Taylor Problems
Gavin Pandya, Steve Shkoller
We derive interface models for 3D Rayleigh-Taylor instability (RTI), making use of a novel asymptotic expansion in the non-locality of the fluid flow. These interface models are de…
Simultaneous development of shocks and cusps for 2D Euler with azimuthal symmetry from smooth data
Tristan Buckmaster, Theodore D. Drivas, Steve Shkoller +1
A fundamental question in fluid dynamics concerns the formation of discontinuous shock waves from smooth initial data. We prove that from smooth initial data, smooth solutions to t…
Shock formation and vorticity creation for 3d Euler
Tristan Buckmaster, Steve Shkoller, Vlad Vicol
We analyze the shock formation process for the 3d non-isentropic Euler equations with the ideal gas law, in which sounds waves interact with entropy waves to produce vorticity. Bui…