38 citations · 72 across the 18 of their papers we have counts for
7 papers · 1 filter
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…
Real analytic local well-posedness for the Triple Deck
Sameer Iyer, Vlad Vicol
The Triple Deck model is a classical high order boundary layer model that has been proposed to describe flow regimes where the Prandtl theory is expected to fail. At first sight th…
The inviscid limit for the Navier-Stokes equations with data analytic only near the boundary
Igor Kukavica, Vlad Vicol, Fei Wang
We address the inviscid limit for the Navier-Stokes equations in a half space, with initial datum that is analytic only close to the boundary of the domain, and has finite Sobolev…
Remarks on a paper by Gavrilov: Grad-Shafranov equations, steady solutions of the three dimensional incompressible Euler equations with compactly supported velocities, and applications
Peter Constantin, Joonhyun La, Vlad Vicol
We describe a method to construct smooth and compactly supported solutions of 3D incompressible Euler equations and related models. The method is based on localizable Grad-Shafrano…