Frank Merle

Mathematician Frank Merle specializes in the qualitative study of nonlinear partial differential equations (PDEs) and the asymptotic time behavior of their solutions. His work focuses on the Hamiltonian case. Early in his career, he worked on the mass-critical nonlinear Schrödinger equation (NLS), which counter-intuitively characterizes singular solutions of smaller mass. He then considers the general size case for NLS and critical generalized Korteweg-De Vries (gKdV). Together with Martel, introducing a restrictive notion of eternal solution (see also work with Zaag), he demonstrates the classical conjecture of singularity formation for gKdV and describes it. With Raphaël, he proved the LogLog conjecture for the generic singularity for NLS, putting an end to a scientific controversy. Over the last twenty years, he has successfully introduced, with Duyckaerts, Kenig, a systematic method for studying the large-time dynamics of PDEs and the soliton resolution conjecture. More recently, with Raphaël, Rodnianski and Szeftel, he described singularities for Euler and compressible Navier-Stoke and gave a surprising counterexample to global existence in the defocusing case. He has been twice awarded the Bocher Prize, the Clay Prize, the Ampère Prize, two conferences, including a plenary, at the International Congress of Mathematicians, a European Resarch Council (ERC) advanced grant and the silver medal of the Centre national de la recherche scientifique (CNRS).

Photo credit: Mathieu Baumer

Page last updated: February 17, 2026