23 citations · 129 across the 19 of their papers we have counts for
5 papers · 2 filters
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…
Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation
Tristan Buckmaster, Pierre Germain, Zaher Hani +1
Consider the cubic nonlinear Schrödinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We…
Convex integration and phenomenologies in turbulence
Tristan Buckmaster, Vlad Vicol
In this review article we discuss a number of recent results concerning wild weak solutions of the incompressible Euler and Navier-Stokes equations. These results build on the grou…