Université de Cergy-Pontoise - IHES Chair in Analysis
Frank Merle is studying the singularities of non-linear partial differential equations. Member at Université de Cergy-Pontoise of the CNRS "Analysis, geometry and modelization" lab (UMR 8088), his research themes that arise out of hard analysis and have an important impact on mathematical physics.
With his ERC Advanced Grant “Blow-Up, Dispersion and Solitons” (Blowdisol), Frank Merle organized a trimester on non-linear waves at IHES in 2016.
This year, Frank Merle worked on different subjects.
The first addressed fluid mechanics. he established and described, for some initial data, the explosion for compressible three-dimensional Navier-Stokes equations. This is the first result of this type.
The second consisted of solving negatively a classical Bourgain conjecture. The question is whether or not the solution with regular data is global for the Schrödinger equation delocalizing on critical. The answer, surprisingly, is no.
Finally, the last working group focused on the resolution of the “solitons resolution conjecture” for the radial critical wave equation in an odd dimension.
Bocher Memorial Prize (2005)
CNRS Silver Medal (2005)
ERC Advanced Grant (2011)
Plenary speaker at ICM Seoul (2014)
"Prix Ampère de l'Électricité de France", Académie des Sciences (2018)
Academia Europaea member