38 citations · 72 across the 11 of their papers we have counts for
19 papers · 1 filter
Exact Boundary Controllability for the Ideal Magneto-hydrodynamic Equations
Igor Kukavica, Matthew Novack, Vlad Vicol
We address the problem of controllability of the MHD system in a rectangular domain with a control prescribed on the side boundary. We identify a necessary and sufficient condition…
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…
Formation of point shocks for 3D compressible Euler
Tristan Buckmaster, Steve Shkoller, Vlad Vicol
We consider the 3D isentropic compressible Euler equations with the ideal gas law. We provide a constructive proof of shock formation from smooth initial datum of finite energy, wi…
Weak solutions of ideal MHD which do not conserve magnetic helicity
Rajendra Beekie, Tristan Buckmaster, Vlad Vicol
We construct weak solutions to the ideal magneto-hydrodynamic (MHD) equations which have finite total energy, and whose magnetic helicity is not a constant function of time. In vie…
Formation of shocks for 2D isentropic compressible Euler
Tristan Buckmaster, Steve Shkoller, Vlad Vicol
We consider the 2D isentropic compressible Euler equations, with pressure law $p(ρ) = (\sfrac{1}γ) ρ^γ$, with . We provide an elementary constructive proof of shock formation…