Advances in Nonlinear Analysis and Nonlinear Waves: a Conference in Honor of Frank Merle

Since his early articles in the 1980s, Frank Merle’s work has been mostly centered on the mathematical analysis of nonlinear partial differential equations with Hamiltonian structure, like dispersive and wave equations, appearing in problems of wave propagation. In the 1980s, basic properties of these equations were established, notably the existence and stability properties of special solutions called solitons.  In the 1990s, the introduction of tools from harmonic analysis led to a refined understanding of the properties of the linear equations and how to extend them to nonlinear equations by perturbation. In this context, breakthrough works on the local well-posedness problem for such equations by Kenig-Ponce-Vega, Bourgain, Tao and others, were extremely influential. In particular, the notion of criticality appeared (invariance by scaling). The remaining problem of understanding qualita- tively the long-time dynamics of solutions, in relation with solitons have attracted considerable interest in the last thirty years. Frank Merle has enormously contributed to such questions in di↵erent directions : blowup in finite time, multi-solitons, collision of solitons, classification of solutions, soliton resolution conjecture. Very often, his surprising and disruptive ideas have strongly influenced the field. During the conference, Pierre Rapha ̈el (Herchel Smith Professor of Pure Mathematics at the University of Cambridge), former PhD student and long-term collaborator of Frank Merle, will give a talk summarizing Merle’s main contributions and ideas.  In this conference, several of the best worldwide experts in the field of dispersive and wave equations will present various aspects of their recent advances.