TMS project: Nonlinear dispersive equations


Copyright: Colourbox


People



  • Arnaud Eychenne (PhD)
  • Razvan Mosincat (Postdoc)
  • Didier Pilod (PI)
  • Martin Paulsen (PhD)
  • Frederic Valet (Postdoc)

  • Project Description


    The research project "Nonlinear dispersive equations: nonlocal operators, dispersive blow-up and the soliton resolution conjecture" (NonDispEq) is founded by Bergens forskningsstiftelse (BFS) and hosted at the Department of Mathematics of the University of Bergen. It was launched in 2018 and aims at expanding our knowledge of dynamic properties of solutions to nonlinear dispersive evolution equations arising in mathematical physics and mathematical fluid mechanics.

    News and Events


  • Group of work to study Pseudo-Differentiel Operators every Wednsday from 14:00 to 16:00 in the Automn 2020
  • Course in Harmonic Analysis MAT331 in the Spring 2020
  • Dispersive Waves and related topics, conference in honor of Gilles Lebeau, Bergen, June 17-21, 2019.
  • Norwegian meeting on PDEs, Trondheim, Norway, June 5-7, 2019.
  • Analysis and PDE seminar at UiB (every Tuesday from 14:15 to 16:00 at UiB)
  • One-day seminar on Geometry, Analysis, and PDE Bergen, October 21, 2018.

  • Publications and Preprints


    1. Finite point blowup for the critical generalized Korteweg-de Vries equation, preprint, (2021), 41 pages, Yvan Martel and Didier Pilod.
    2. Global well-posedness and scattering for the Dysthe equation in L^2, Journal de Mathématiques Pures et Appliquées, 149 (2021), 73-97, Razvan Mosincat, Didier Pilod and Jean-Claude Saut.
    3. Dispersive estimates for full dispersion KP equations, Journal of Mathematical Fluid Mechanics, 23, Article number: 25 (2021), 24 pages, Didier Pilod, Jean-Claude Saut, Sigmund Selberg and Achenef Tesfahun.
    4. On the unique continuation of solutions to non-local non-linear dispersive equations, Commmunications in Partial Differential Equations, 45 (2020), 872-886, Carlos Kenig, Didier Pilod, Gustavo Ponce and Luis Vega.
    5. Full family of flattening solitary waves for the mass critical generalized KdV equation, Commmunications in Mathematical Physics, 378, (2020),1011-1080, Yvan Martel and Didier Pilod.
    6. On the local well-posedness for a full dispersion Boussinesq system with surface tension, Proceedings of the American Mathematical Society, 147 (2019), 2545-2559, Henrik Kalisch and Didier Pilod.

    Collaborators


  • Miguel Alejo (Universidad de Cordoba);
  • Jerry Bona (University of Illinois at Chicago);
  • Adan Corcho (Universidade Federal do Rio de Janeiro);
  • Raphaël Côte (Universite de Strasbourg);
  • Mats Ehrnstrom (NTNU Trondheim);
  • Henrik Kalisch (University of Bergen);
  • Carlos Kenig (University of Chicago);
  • Felipe Linares (IMPA Rio de Janeiro);
  • Luc Molinet (Universite de Tours);
  • Claudio Munoz (Universidade de Chile);
  • Yvan Martel (Ecole Polytechnique);
  • Gustavo Ponce (University of California, Santa Barbara);
  • Jean-Claude Saut (Universite Paris Sud);
  • Sigmund Selberg (University of Bergen);
  • Achenef Tesfahun (University of Bergen);
  • Luis Vega (BCAM/EHU Bilbao) ;
  • Stephane Vento (Universite Paris 13).

  • Scientific Visits at UiB


  • Yvan Martel (Ecole Polytechnique) from 01/08/2020 to 15/08/2020.
  • Miguel Alejo (Universidad de Cordoba) from 08/03/2020 to 13/03/2020.
  • Adan Corcho (Universidade Federal do Rio de Janeiro) from 02/16/2020 to 15/03/2020.
  • Frederic Valet (Universite de Strasbourg) from 24/02/2020 to 28/02/2020.
  • Jacek jendrej (Universite Paris 13) from 17/02/2020 to 20/02/2020.
  • Luc Molinet (Universite de Tours) and Stephane Vento (Universite Paris 13) from 15/09/2019 to 20/05/2019.
  • Adan Corcho (Universidade Federal do Rio de Janeiro) from 24/08/2019 to 01/09/2019.
  • Felipe Linares (Instituto de Matematica Pura e Aplicada) from 17/06/2019 to 27/06/2019.
  • Jerry Bona (University of Illinois at Chicago) and Hongqiu Chen (University of Menphis) from 11/05/2019 to 18/05/2019.
  • Claudio Munoz (Universidade de Chile) from 05/05/2019 to 11/05/2019.
  • Vinh Nguyen (Ecole Polytechnique) from 20/10/2018 to 27/10/2018.
  • Mats Ehrnstrom (NTNU) from 21/10/2018 to 22/10/2018.
  • Razvan Mosincat (University of Edingburgh) from 18/09/2018 to 20/09/2018.
  • Jean-Claude Saut (Universite Paris Sud) from 04/06/2018 to 08/06/2018.
  • Miguel Alejo (Federal University of Santa Catarina) from 23/04/2018 to 01/05/2018.


  • Conferences and Scientific Visits outside of UiB


  • Didier Pilod gave a talk at the Analysis Seminar, University of Edinburgh, on 27/01/2020.
  • Didier Pilod gave a talk at the 4th Workshop on Nonlinear Dispersive Equations, Federal University of Rio de Janeiro, from 05/11/2019 to 08/11/2019.
  • Didier Pilod gave a talk at the Control and Dynamics of Partial Differential Equations in Strasbourg, University of Strasbourg, from 28/10/2019 to 31/10/2019.
  • Didier Pilod visited the Ecole Polytechnique from 22/09/2019 to 28/09/2019.
  • Didier Pilod gave a minicourse at the Nordfjordeid Summer School 2019 - Analysis, Geometry and PDE, Nordfjordeid (Norway) from 01/07/2019 to 05/07/2019.
  • Arnaud Eychenne gave a talk at the Nonlinear Dispersive Waves, Solitons, and Related Topics Conference, Mittag-Leffer Institute (Sweden) from 10/06/2019 to 14/06/2019.
  • Razvan Mosincat gave a talk at the Norwegian meeting on PDEs, NTNU (Trondheim) from 05/06/2019 to 07/06/2019.
  • Didier Pilod gave a talk at the 2019 Workshop on Nonlinear Dispersive Partial Differential Equations and Inverse Scattering, Fields Institute (Toronto) from 21/05/2019 to 24/05/2019.
  • Didier Pilod gave a talk at the 10th Itinerant Workshop on PDEs, INDAM (Roma Sapienza) from 30/01/2019 to 01/02/2019.
  • Didier Pilod gave a talk at the Workshop on "Dispersion and Integrability", Wolfgang Pauli Institute (Vienna) from 02/10/2018 to 05/10/2018.
  • Didier Pilod gave a talk at the NTNU Workshop on PDEs, Tromndheim from 21/11/2018 to 23/11/2018.
  • Didier Pilod attended the 2018 International Congress of Mathematicians in Rio de Janeiro from 01/08/2018 to 09/08/2018.
  • Didier Pilod gave a talk at the Nonlinear Dispersive Equations, 2018 International Congress of Mathematicians – Sattelite Meeting, Florianopolis (Brazil) from 27/07/2018 to 30/07/2018.
  • Didier Pilod gave a talk at the Lund Workshop on Fluid Dynamics and Dispersive Equations, Lund (Sweden) from 25/06/2018 to 29/06/2018.