Tristan Buckmaster

Assistant Professor,
Department of Mathematics
Princeton University,
Fine Hall, Room 608
Princeton, NJ 08544

buckmaster at math dot princeton dot edu


CV Publications Teaching

About

My main area of interest are Partial Differential Equations with a particular focus on equations related to fluid dynamics. I was a recipient of a 2019 Clay Research Award. My research is supported by the National Science Foundation grant DMS-1900149 'Analytic Methods in Hydrodynamic and Wave Turbulence' and the Simons Foundation Mathematical and Physical Sciences collaborative grant 'Wave Turbulence'. Quanta Magazine wrote a popular science article on a recent paper I wrote in collaboration with Vlad Vicol entitled 'Mathematicians Find Wrinkle in Famed Fluid Equations'.

Publications

T. Buckmaster, T. Drivas, S. Shkoller and V. Vicol, Simultaneous development of shocks and cusps for 2D Euler with azimuthal symmetry from smooth data, preprint

T. Buckmaster, N. Masmoudi, M. Novack and V. Vicol, Non-conservative H^{1/2−} weak solutions of the incompressible 3D Euler equations, submitted

T. Buckmaster and V. Vicol, Convex integration constructions in hydrodynamics, Bulletin of the AMS, 2021

T. Buckmaster and S. Iyer, Formation of unstable shocks for 2D isentropic compressible Euler, submitted

T. Buckmaster, S. Shkoller and V. Vicol, Shock formation and vorticity creation for 3d Euler, submitted

T. Buckmaster and V. Vicol, A Heuristic Approach to Convex Integration for the Euler Equations, Progress in Mathematical Fluid Dynamics, 2020

T. Buckmaster, S. Shkoller and V. Vicol, Formation of point shocks for 3D compressible Euler, submitted

R. Beekie, T. Buckmaster and V. Vicol, Weak solutions of ideal MHD which do not conserve magnetic helicity, Annals of PDE, 2020

T. Buckmaster, P. Germain, Z. Hani, J. Shatah, On the kinetic wave turbulence description for NLS, Quarterly of Applied Mathematics, to appear

T. Buckmaster, S. Shkoller and V. Vicol, Formation of shocks for 2D isentropic compressible Euler, submitted, Communications on Pure and Applied Mathematics, to appear

T. Buckmaster, P. Germain, Z. Hani, J. Shatah, Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation, Inventiones Mathematicae, 2021

T. Buckmaster and V. Vicol, Convex integration and phenomenologies in turbulence, European Mathematical Society, Surveys in Mathematical Sciences, 2019

T. Buckmaster, M. Colombo, V. Vicol, Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1, Journal of European Mathematical Society, to appear

T. Buckmaster, A. Nahmod, G. Staffilani, K. Widmayer, The Surface Quasi-Geostrophic Equation with Random Diffusion, International Mathematics Research Notices, 2018

T. Buckmaster and V. Vicol, Nonuniqueness of weak solutions to the Navier-Stokes equation, Annals of Mathematics, 2019

T. Buckmaster, C. De Lellis, L. Székelyhidi Jr. and V. Vicol, Onsager's conjecture for Admissible Weak Solutions, Communications on Pure and Applied Mathematics, 2019

T. Buckmaster, P. Germain, Z. Hani, J. Shatah, Analysis of (CR) in higher dimension, International Mathematics Research Notices, 2017

T. Buckmaster, P. Germain, Z. Hani, J. Shatah, Effective dynamics of the nonlinear Schrödinger equation on large domains, Communications on Pure and Applied Mathematics, 2018

T. Buckmaster, S. Shkoller and V. Vicol, Nonuniqueness of weak solutions to the SQG equation, Communications on Pure and Applied Mathematics, 2019

T. Buckmaster, C. De Lellis and L. Székelyhidi Jr., Dissipative Euler flows with Onsager-critical spatial regularity , Communications on Pure and Applied Mathematics, 2016

T. Buckmaster, Onsager's conjecture almost everywhere in time, Communications in Mathematical Physics, 2015

T. Buckmaster, C. De Lellis, P. Isett and L. Székelyhidi Jr., Anomalous dissipation for 1/5-Hölder Euler flows, Annals of Mathematics, 2015

T. Buckmaster, C. De Lellis and L. Székelyhidi Jr., Transporting microstructure and dissipative Euler flows, preprint 2013

T. Buckmaster and H. Koch, The Korteweg-de-Vries equation at H^{-1} regularity, Annales IHP-ANL, 2015

T. Buckmaster, Onsager's Conjecture, PhD Thesis, 2014

Teaching

Under construction.