Mardi 11 Octobre
Heure: 
13:30  14:30 
Lieu: 
Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13 
Résumé: 
PM  EDP  Statistical mechanics of wave maps in dimension 1+1  
Description: 
Jacek JendrejI will present a recent joint work with Brzezniak.We study wave maps with values in S^d, defined on the future light cone {x &lt;= t}, with prescribed data at the boundary {x = t}. Based on the work of Keel and Tao, we prove that the problem is wellposed for locally absolutely continuous boundary data. We design a discrete version of the problem and prove that for every absolutely continuous boundary data, the sequence of solutions of the discretised problem converges to the corresponding continuous wave map as the mesh size tends to 0. Next, we consider the boundary data given by the S^dvalued Brownian motion. We prove that the sequence of solutions of the discretised problems has an accumulation point for the topology of locally uniform convergence. We argue that the resulting random field can be interpreted as the wavemap evolution corresponding to the initial data given by the Gibbs distribution. 

