A Clay Research Award is made to Frank Merle (IHES, Paris), Pierre Raphaël (Cambridge), Igor Rodnianski (Princeton), and Jérémie Szeftel (Sorbonne Université, Paris). The award is made in recognition of their profound contributions to the theory of nonlinear partial differential equations.
Merle, Raphaël, Rodnianski and Szeftel are recognised, in particular, for their groundbreaking advances in the understanding of singular solutions to the fundamental equations of fluid dynamics, including their construction of smooth self-similar solutions for the compressible Euler equation, and families of finite-energy blow-up solutions for both the compressible Euler and Navier-Stokes equations.
They are also recognised for establishing the existence of finite energy blow-up solutions, arising from smooth initial data, for the energy supercritical defocusing nonlinear Schrödinger equation (NLS) in a spectacular work that resolves a longstanding conjecture of Bourgain. Their discovery of a startling connection between the fundamental equations of fluid mechanics and the NLS has opened a new vista in the field of nonlinear partial differential equations.