Webpage of Louise GASSOT

About

I am a CNRS researcher at IRMAR (Rennes, France).

- 2022-2023: postdoc at the University of Basel with Enno Lenzmann

- 2021-2022: Institute postdoc at ICERM (Brown University)

- 2018-2021: PhD under the supervision of Patrick Gérard at the Laboratoire de Mathématiques d'Orsay (LMO).

Research topics

I am interested in the long time behavior of solutions to dispersive nonlinear PDEs. I mainly focus on PDEs with weak dispersion (for instance, the Schrödinger equation on the Heisenberg group) and on integrable PDEs (for instance, the Benjamin-Ono equation). Here is a lay summary of the zero-dispersion limit problem for the Benjamin-Ono equation on the torus.

PhD student

Starting 2025 : Thomas Courant (co-supervision with Miguel Rodrigues)

Funding

2024-2029 : Member of project HEAD (Hyperbolic Equations, Asymptotics & Dynamics), funded by the French ANR. Scientific coordinator: Miguel Rodrigues.

Publications

Benjamin-Ono equation on the line :
   - explicit formula for rational data, long-time behavior [BGGM24a]
   - zero-dispersion limit [BGGM24b], [BGM25] and proceeding [BGGM24]

Benjamin-Ono equation on the torus :
   - long-time behavior of perturbations [GL25], [G22]
   - zero-dispersion limit [G23b], [G23a]
   - hierarchy [G21b]

Cauchy problem in low regularity for Schrödinger type equations :
   - pathological set [CG25], [CG23]
   - probabilistic local well-posedness [CGI24], [GL22] and proceeding [CGI22]

Stability of traveling waves for the Schrödinger equation on the Heisenberg group: [G21a], [G20]

Articles

Pdf	Title	Co-authors	Journal
[GL25]	Global well-posedness for the ILW equation in H^s(T) for s>-1/2	Thierry Laurens
[BGGM24b]	The Benjamin-Ono equation in the zero-dispersion limit for rational initial data: generation of dispersive shock waves	Elliot Blackstone, Patrick Gérard, Peter D. Miller
[BGGM24a]	The Benjamin-Ono Initial-Value Problem for Rational Data with Application to Long-Time Asymptotics and Scattering	Elliot Blackstone, Patrick Gérard, Peter D. Miller	to appear in Ann. Inst. H. Poincaré C Anal. Non Linéaire
[BGM25]	On Strong Zero-Dispersion Asymptotics for Benjamin-Ono Soliton Ensembles	Elliot Blackstone, Peter D. Miller	Contemp. Math., 823:213-270, 2025.
[CG25]	Pathological set with loss of regularity for nonlinear Schrödinger equations	Rémi Carles	Ann. Inst. H. Poincaré C Anal. Non Linéaire, 42(3):715–753, 2025.
[CGI24]	Refined probabilistic local well-posedness for a cubic Schrödinger half-wave equation	Nicolas Camps, Slim Ibrahim	J. Differential Equations, 380:443--490, 2024.
[G23b]	Lax eigenvalues in the zero-dispersion limit for the Benjamin-Ono equation on the torus		SIAM J. Math. Anal., 55(5):5782-5822, 2023.
[G23a]	Zero-dispersion limit for the Benjamin-Ono equation on the torus with single well initial data		Comm. Math. Phys., 401:2793–2843, 2023.
[CG23]	Pathological set of initial data for scaling-supercritical nonlinear Schrödinger equations	Nicolas Camps	Int. Math. Res. Not. IMRN, 2023(15):13214–13254, 2023.
[GL22]	Probabilistic local well-posedness for the Schrödinger equation posed for the Grushin operator	Mickaël Latocca	J. Funct. Anal., 283(3):109519, 2022.
[G22]	Long time behavior of solutions for a damped Benjamin-Ono equation		Math. Z., 300:1939--2006, 2022.
[G21b]	The third order Benjamin-Ono equation on the torus: well-posedness, traveling waves and stability		Ann. Inst. H. Poincaré C Anal. Non Linéaire, 38(3):815--840, 2021.
[G21a]	On the orbital stability of a family of traveling waves for the cubic Schrödinger equation on the Heisenberg group		Bull. Soc. Math. France, 149(1):15--54, 2021.
[G20]	On the radially symmetric traveling waves for the Schrödinger equation on the Heisenberg group		Pure Appl. Anal., 2(4):739--794, 2020.

Proceedings

Pdf	Title	Co-authors	Journal
[BGGM23]	Zero-dispersion limit for the Benjamin-Ono equation	Elliot Blackstone, Patrick Gérard, Peter D. Miller	Séminaire Laurent Schwartz — EDP et applications, 2023-2024, Talk no. 6, 16 p.
[CGI22]	Cubic Schrödinger half-wave equation and random initial data	Nicolas Camps, Slim Ibrahim	Journées équations aux dérivées partielles, 2022.
[PhD]	Long-time behavior of solutions to nonlinear PDEs: orbital stability of traveling waves, dispersion, integrability, damping		PhD manuscript, 2021.