Asymptotic self-similar blow-up profile for three-dimensional axisymmetric Euler equations using neural networks

no code implementations • 18 Jan 2022 • Yongji Wang, Ching-Yao Lai, Javier Gómez-Serrano, Tristan Buckmaster

Whether there exist finite time blow-up solutions for the 2-D Boussinesq and the 3-D Euler equations are of fundamental importance to the field of fluid mechanics.

Non-conservative $H^{\frac 12-}$ weak solutions of the incompressible 3D Euler equations

no code implementations • 22 Jan 2021 • Tristan Buckmaster, Nader Masmoudi, Matthew Novack, Vlad Vicol

For any positive regularity parameter $\beta < \frac 12$, we construct non-conservative weak solutions of the 3D incompressible Euler equations which lie in $H^{\beta}$ uniformly in time.

Analysis of PDEs

Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation

no code implementations • 8 Jul 2019 • Tristan Buckmaster, Pierre Germain, Zaher Hani, Jalal Shatah

Consider the cubic nonlinear Schr\"odinger equation set on a d-dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent.

Analysis of PDEs Mathematical Physics Mathematical Physics