TMS project: Nonlinear dispersive equations

Copyright: Colourbox


Local members:

  • Arnaud Eychenne (PhD)
  • Razvan Mosincat (Postdoc)
  • Didier Pilod (PI)

  • 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

  • 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. Global well-posedness and scattering for the Dysthe equation in L^2, preprint (2020), 20 pages, joint with Razvan Mosincat and Jean-Claude Saut.
    2. Dispersive estimates for full dispersion KP equations, preprint (2020), 29 pages, joint with Jean-Claude Saut, Sigmund Selberg and Achenef Tesfahun.
    3. On the unique continuation of solutions to non-local non-linear dispersive equations, Comm. Part. Diff. Eq., 45 (2020), 872-886, joint with Carlos Kenig, Gustavo Ponce and Luis Vega.
    4. Full family of flattening solitary waves for the mass critical generalized KdV equation, to appear in Comm. Math. Phys., (2020), 70 pages, joint with Yvan Martel.
    5. On the local well-posedness for a full dispersion Boussinesq system with surface tension, Proc. Amer. Math. Soc., 147 (2019), 2545-2559, Henrik Kalisch and Didier Pilod.


    Scientific Visits at UiB

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

  • Conferences and Scientific Visits outside of UiB

  • 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.
  • 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 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 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 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 2019 Workshop on Nonlinear Dispersive Partial Differential Equations and Inverse Scattering, Fields Institute (Toronto) from 21/05/2019 to 24/05/2019.
  • Razvan Mosincat gave a talk at the Norwegian meeting on PDEs, NTNU (Trondheim) from 05/06/2019 to 07/06/2019.
  • 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.
  • 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.