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SINGWAVES SIGNED

Singularity formation in nonlinear evolution equations

Total Cost €

EC-Contrib. €

Partnership

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Outcomes and
results

SINGWAVES project word cloud

Explore the words cloud of the SINGWAVES project. It provides you a very rough idea of what is the project "SINGWAVES" about.

discovery mechanics solitary equations connection group fundamental odinger concentration played packets optics phenomenon intense schr nonlinear waves frontier wave mysterious singular energy made class singwaves setting central mostly canonical existence dynamics ago huge fluid packet corresponds investigation bubbles linear classification deeply description progress exploration international directions works models physics singularity construction ten strenghten

Project "SINGWAVES" data sheet

The following table provides information about the project.

Coordinator	THE CHANCELLOR MASTERS AND SCHOLARSOF THE UNIVERSITY OF CAMBRIDGE Organization address address: TRINITY LANE THE OLD SCHOOLS city: CAMBRIDGE postcode: CB2 1TN website: www.cam.ac.uk contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.
Coordinator Country	United Kingdom [UK]
Total cost	1˙211˙055 €
EC max contribution	1˙211˙055 € (100%)
Programme	1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
Code Call	ERC-2014-CoG
Funding Scheme	ERC-COG
Starting year	2015
Duration (year-month-day)	from 2015-08-01 to 2020-07-31

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	THE CHANCELLOR MASTERS AND SCHOLARSOF THE UNIVERSITY OF CAMBRIDGE THE CHANCELLOR MASTERS AND SCHOLARSOF THE UNIVERSITY OF CAMBRIDGE Organization address address: TRINITY LANE THE OLD SCHOOLS city: CAMBRIDGE postcode: CB2 1TN website: www.cam.ac.uk contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	UK (CAMBRIDGE)	coordinator	92˙323.00
2	UNIVERSITE DE NICE SOPHIA ANTIPOLIS UNIVERSITE DE NICE SOPHIA ANTIPOLIS Organization address address: AVENUE VALROSE 28 GRAND CHATEAU city: NICE postcode: 6100 website: www.unice.fr contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	FR (NICE)	participant	1˙118˙731.00

Map

Project objective

'Non linear wave equations are central in the description of many canonical models in physics from nonlinear optics to fluid mechanics. A phenomenon of particular interest is singularity formation which corresponds to the concentration of the energy of the wave packet. The existence and description of such dynamics is still mostly mysterious, but fundamental progress have been made in the past ten years on canonical models like nonlinear wave and Schr'odinger equations, with in particular the discovery of the fundamental role played by a specific class of nonlinear wave packets: the solitary waves. These very recent works open up a huge field of investigation on problems which were considered out of reach ten years ago. The aim of the SINGWAVES project is to strenghten our research group in the setting of an intense international activity with two main directions of investigation: the construction and classification of singular bubbles for some canonical models like non linear Schr'odinger equations, the exploration of new deeply nonlinear dynamics in connection with classical models at the frontier of current research. '

Publications

List of publications.
year	authors and title	journal	last update
2017	Mahir Hadzic and Pierre Raphael Melting and freezing for the 2D radial Stefan problem published pages: , ISSN: 1435-9863, DOI:	Journal of the European Mathematical society	2020-01-21
2017	Charles Collot, Frank Merle, Pierre RaphaÃ«l Dynamics Near the Ground State for the Energy Critical Nonlinear Heat Equation in Large Dimensions published pages: 215-285, ISSN: 0010-3616, DOI: 10.1007/s00220-016-2795-4	Communications in Mathematical Physics 352/1	2020-01-21
2018	Patrick Gerard, Enno Lenzman, Oana Pocovnicu and Pierre Raphael A two soliton with transient turbulent regime for the cubic half wave on the real line published pages: , ISSN: 2199-2576, DOI:	Annals of PDE	2020-01-21
2017	Yvan Martel and Pierre Raphael Strongly interacting blow up bubbles for the mass critical NLS published pages: , ISSN: 0012-9593, DOI:	Annales scientifiques de l\'ecole normale supÃ©rieure	2020-01-21
2018	Ivan Naumkin and Thierry Cazenave Modified scattering for the critical nonlinear Schrodinger equation published pages: , ISSN: 0022-1236, DOI:	Journal of functional analysis	2020-01-21
2017	Charles Collot Nonradial type II blow up for the energy-supercritical semilinear heat equation published pages: 127-252, ISSN: 2157-5045, DOI: 10.2140/apde.2017.10.127	Analysis & PDE 10/1	2020-01-21
2016	Charles Collot, Jeremie Szeftel and Pierre Raphael On the stability of type I blow up for the energy super critical heat equation published pages: , ISSN: 0065-9266, DOI:	Memoirs of the American Mathematical Society	2020-01-21
2017	C. Lu and J. Zheng The radial defocusing energy-supercritical NLS in dimension four, published pages: , ISSN: 0022-0396, DOI:	Journal of Differential equations	2020-01-21

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The information about "SINGWAVES" are provided by the European Opendata Portal: CORDIS opendata.