Description
2026 Breakthrough Prize in Mathematics laureate Frank Merle’s work has significantly advanced the modern understanding of nonlinear evolution equations – the mathematical descriptions of how waves, fluids, and other dynamic systems change over time. His work has a particular focus on singularities: points where solutions to the equations surge to infinity. Alone and in collaborations, he has solved several fundamental problems, including proving that certain equations long thought to be well-behaved actually “blow up” – become infinite – in finite time.
Watch Sergey Brin and GG Soto award Merle the Breakthrough Prize: https://youtu.be/Kv_uLctQT9k
Working on the soliton resolution conjecture (which predicts that any wave disturbance will eventually decompose into a set of stable, shape-preserving waves), Merle and Carlos Kenig, joined later by Thomas Duyckaerts, developed the powerful channels of energy technique coupled with the concentration compactness method. With Yvan Martel and Pierre Raphael, he revealed how singularities form in the KdV type equation (which describes various wave phenomena from shallow waves to rogue waves). Perhaps most remarkable is his work on the nonlinear version of the famous Schrödinger equation from quantum physics. In early work, he made a complete classification of all the ways this equation’s solutions can blow up. Later he proved, with Pierre Raphael, Igor Rodnianski, and Jérémie Szeftel, that the defocusing version of the equation – long believed to be inherently stable – can in fact blow up in finite time. This highly surprising result exploited an unexpected connection to fluid dynamics: it helped to resolve a major open problem, identifying smooth solutions to the compressible Euler and Navier-Stokes equations where the fluid’s density and velocity become infinite – representing a complete breakdown of the fluid description. Throughout his career, Merle’s insights have overturned fundamental assumptions in the field, forged deep connections between mathematics and physics, and opened new avenues toward some of the most celebrated unsolved problems.