The 2019 Clay Research Award to Tristan Buckmaster (Princeton), Philip Isett (Caltech) and Vlad Vicol (NYU) is made in recognition of the profound contributions that each of them has made to the analysis of partial differential equations, particularly the Navier-Stokes and Euler equations.
Buckmaster and Vicol changed perceptions of the nature of weak solutions to the Navier-Stokes equations by proving that such solutions can be remarkably wild – severely non-smooth and highly non-unique.
With a series of breakthroughs, Isett finally settled Onsager’s 1949 Conjecture that, in turbulent regimes, below a specific regularity threshold, solutions to Euler’s equations can be energy dissipative.
Both works solve longstanding problems of fundamental importance. In the course of doing so, they introduce novel ideas in hard analysis, building on the program of De Lellis and Székelyhidi, inspired by the pioneering work of Nash and Gromov.