Resumen de Global existence for energy critical waves in $3$-d domains

Nicolas Burq, Gilles Lebeau, Fabrice Planchon

• We prove that the defocusing quintic wave equation, with Dirichlet boundary conditions, is globally well posed on for any smooth (compact) domain . The main ingredient in the proof is an spectral projector estimate, obtained recently by Smith and Sogge, combined with a precise study of the boundary value problem.