Annuaire
The annual meeting of the ANR project Smooth
June 11, 12, 13 the annual meeting of the ANR project Smooth will take place at UMPA. There will be a mini-cours by N. Camps on the random averaging operator method introduced by Yu Deng et al. and talks by V. Issa, M Ifrim, P. Mackowiak, D. Tataru and Chenmin Sun.
The talks will take place at Amphi A.
Here is the program with the titles :
Wednesday, June 11 :
14h-15h M. Ifrim : The small data global well-posedness conjecture for defocusing dispersive flows.
Abstract : Providing a better description of the global dynamics for nonlinear dispersive PDE's has been the focus of many experts in the field for a long time. One fundamental property in this regard is \emph{scattering}, which asserts that asymptotically the solutions to the nonlinear flow approach solutions to a corresponding linear flow. Scattering results have been proved for many nonlinear dispersive flows in cases where the nonlinear interactions are relatively mild due to the dispersive decay. However, there are also many models where the nonlinear interactions are too strong to allow for classical scattering, and where nonperturbative interactions are seen at all large time scales. Notably, this includes all cubic problems in 1D, for which global results have only been proved under the assumption that the initial data is both smooth, small and localized. However, except for the completely integrable case, until very recently no such results have been known for small but non-localized initial data, and indeed there was not even an indication that this might be at all possible. This talk will present our recent conjecture, which broadly asserts that small data should yield global solutions for 1D defocusing dispersive flows with cubic nonlinearities, in both semilinear and quasilinear settings. So far we were able to prove the conjecture in several settings, which will be described. Finally, we will also discuss the higher dimensional counterpart of this conjecture, which is most interesting in 2D. This is joint work with Daniel Tataru.
15h-15h30 Coffee break
15h30-16h30 N. Camps : Gibbs Measures and Invariant Dynamics for NLS equations in 2D (1)
Thursday, June 12 :
9h-10h : N. Camps : Gibbs Measures and Invariant Dynamics for NLS equations in 2D (2)
10h-10h30 Coffee break
10h30-11h30 D. Tataru : Low regularity solutions in quasilinear dispersive flows.
Abstract : The aim of this talk will be to provide an overview of recent ideas and methods developed recently in the study of quasilinear dispersive flows at low regularity.
14h-15h P. Mackowiak (TBA)
15h-15h30 Coffee break
15h30-16h30 N. Camps Gibbs Measures and Invariant Dynamics for NLS equations in 2D (3)
Friday, June 13 :
9h-10h : Chenmin Sun : Probabilistic Cauchy theory for the cubic NLS on the 2-sphere
10h-10h30 Coffee break
10h30-11h30 V. Issa : Statistical physics and Hamilton-Jacobi equations in infinite dimensions