AGM

BLOWDISOL - Overview

ERC Advanced Grant

Project acronym: BLOWDISOL
Project full title: BLOW UP, DISPERSION AND SOLITONS
Grant agreement no.: 291214
Duration: 60 months
Start : April 2012

Principal Investigator: Franck Merle (see below)
Host Institution: Université de Cergy-Pontoise (UCP), France
Research Unit at UCP: UMR 8088 Analyse, géométrie et modélisation also associated to the CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE
PIC Number: 999997930

Proposal Summary

Many physical models involve nonlinear dispersive problems, like wave or laser propagation, plasmas, ferromagnetism, etc. So far, the mathematical understanding of these equations is rather poor. In particular, we know little about the detailed qualitative behavior of their solutions. Our point is that an apparent complexity hides universal properties of these models; investigating and uncovering such properties has started only recently. More than the equations themselves, these universal properties are essential
for physical modelisation.

By considering several standard models such as the nonlinear Schrodinger, nonlinear wave, generalized KdV equations and related geometric problems, the goal of this proposal is to describe the generic global behavior of the solutions and the profiles which emerge either for large time or by concentration due to strong nonlinear effects, if possible through a few relevant solutions (sometimes explicit solutions, like solitons). In order to do this, we have to elaborate different mathematical tools depending on the context and the specificity of the problems. Particular emphasis will be placed on:

- large time asymptotics for global solutions, decomposition of generic solutions into sums of decoupled solitons in non integrable situations,
- description of critical phenomenon for blow up in the Hamiltonian situation, stable or generic behavior for blow up on critical dynamics, various relevant regularisations of the problem,
- global existence for defocusing supercritical problems and blow up dynamics in the focusing cases.

Contact

ERC BLOWDISOL
UCP - Labo. AGM
2 av. Adolphe Chauvin
95302 CERGY-PONTOISE CEDEX

Principal Investigator: Frank Merle (frank.merle @ u-cergy.fr)

Administrative: Linda Isone

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