24 | IHES Annual Report 2020

Frank MERLE Mathematics, professor, Université de Cergy-Pontoise.

This year, FRANK MERLE, worked in different working groups. 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 in solving negatively a classical Bourgain conjecture. The question being 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 odd dimension.

SCIENTIFIC ACTIVITY

DISTINCTIONS

Bocher Memorial Prize (2005) CNRS Silver Medal (2005) ERC Advanced Grant "Blow Up, Dispersion and Solitons" (Blowdisol) (2011) Plenary speaker ICM (2014) Prix Ampère de l'Électricité de France, Académie des sciences de Paris (2018) Academia Europaea, member (2020)

Editor of: Les Publications Mathématiques de l IHES Analysis and PDE Journal of Hyperbolic Equation Bulletin des Sciences Math. Journal de l'École polytechnique

CONFERENCES

China (PR.) PDE Seminar via Zoom, ShanghaiTech University, Shanghai (19 November) On the Implosion of a Three Dimensional Compressible Fluid (seminar)

France Ladhyx, École polytechnique, Palaiseau (28 February) On the Implosion of a Three Dimensional Compressible Fluid (seminar)

Video conference One World PDE Seminar, University of Bath and La Sapienza Università di Roma (26 May) On the Implosion of a Three Dimensional Compressible Fluid (video conference)

PUBLICATIONS

With T. Duyckaerts and C. Kenig Exterior Energy Bounds for the Critical Wave Equation Close to the Ground State Commun. Math. Phys. 379 (2020), 1113-1175.

On Strongly Anisotropic Type I Blowup Int. Math. Res. Not. IMRN, vol. 2020, n°2, 541-606.

With C. Collot and P. Raphaël Strongly Anisotropic Type II Blow Up at an Isolated Point J. Amer. Math. Soc. 33(2), 527-607.

Université de Cergy Pontoise IHES Analysis Chair