Singularity formation in nonlinear evolution equations

Project Information

SINGWAVES

Grant agreement ID: 646650

DOI 10.3030/646650

Project closed

EC signature date 4 May 2015

Start date 1 August 2015

End date 31 January 2021

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost € 1 211 055,00

EU contribution € 1 211 055,00

Coordinated by

THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE
United Kingdom

Publications

Other (4)

Self-similar blow-up profiles for slightly supercritical nonlinear Schrödinger equations

Author(s): Martel and Raphael
Published in: 2019
Publisher: Archiv for math

On weakly turbulent solutions to the perturbed linear Harmonic oscillator

Author(s): Faou and Raphael
Published in: 2020
Publisher: Archiv for math

On the implosion of a three dimensional compressible fluid

Author(s): Merle, Raphael, Rodnianski and Szeftel
Published in: 2019
Publisher: Archiv for math

On blow up for the energy super critical defocusing non linear Schrödinger equations

Author(s): Merle, Raphael, Rodnianski, Szeftel
Published in: 2019
Publisher: Archiv for math

Peer reviewed articles (11)

Strongly anisotropic type II blow up at an isolated point

Author(s): Collot, Merle and Raphael
Published in: Jour. Amer. Math. Soc, 2020, Page(s) 541–606, ISSN 1073-7928
Publisher: Oxford University Press

On strongly anisotropic type I blowup

Author(s): Merle, Raphael, Szeftel
Published in: IMRN, 2020, ISSN 1073-7928
Publisher: Oxford University Press

On traveling waves of the nonlinear Schrödinger equation escaping a potential well

Author(s): Naumkin and Raphael
Published in: Ann. Henri Poincare, 2020, Page(s) 1677–1758, ISSN 1424-0637
Publisher: Birkhauser Verlag

A two soliton with transient turbulent regime for the cubic half wave on the real line

Author(s): Patrick Gerard, Enno Lenzman, Oana Pocovnicu and Pierre Raphael
Published in: Annals of PDE, 2018, ISSN 2199-2576
Publisher: springer

On the stability of type I blow up for the energy super critical heat equation

Author(s): Charles Collot, Jeremie Szeftel and Pierre Raphael
Published in: Memoirs of the American Mathematical Society, 2016, ISSN 0065-9266
Publisher: American Mathematical Society

Modified scattering for the critical nonlinear Schrodinger equation

Author(s): Ivan Naumkin and Thierry Cazenave
Published in: Journal of functional analysis, 2018, ISSN 0022-1236
Publisher: Academic Press

The radial defocusing energy-supercritical NLS in dimension four,

Author(s): C. Lu and J. Zheng
Published in: Journal of Differential equations, 2017, ISSN 0022-0396
Publisher: Academic Press

Strongly interacting blow up bubbles for the mass critical NLS

Author(s): Yvan Martel and Pierre Raphael
Published in: Annales scientifiques de l'ecole normale supérieure, 2017, ISSN 0012-9593
Publisher: Elsevier BV

Melting and freezing for the 2D radial Stefan problem

Author(s): Mahir Hadzic and Pierre Raphael
Published in: Journal of the European Mathematical society, 2017, ISSN 1435-9863
Publisher: european math society

Nonradial type II blow up for the energy-supercritical semilinear heat equation

Author(s): Charles Collot
Published in: Analysis & PDE, Issue 10/1, 2017, Page(s) 127-252, ISSN 2157-5045
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/apde.2017.10.127

Dynamics Near the Ground State for the Energy Critical Nonlinear Heat Equation in Large Dimensions

Author(s): Charles Collot, Frank Merle, Pierre Raphaël
Published in: Communications in Mathematical Physics, Issue 352/1, 2017, Page(s) 215-285, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-016-2795-4