Seminar

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Abstract: In this talk we discuss the almost-global well-posedness of a wide class of coupled Wave-Klein-Gordon equations in 2+1 space-time dimensions, when initial data are small and localized. The Wave-Klein-Gordon systems arise from several physical models especially related to General Relativity but few results are known at present in lower space-time dimensions. Compared with prior related results, we here consider a strong quadratic quasilinear coupling between the wave and the Klein-Gordon equation and no restriction is made on the support of the initial data which are supposed to only have a mild decay at infinity and very limited regularity. Our proof relies on a combination of energy estimates localized to dyadic space-time regions and pointwise interpolation type estimates within the same regions. This is akin to ideas previously used by Metcalfe-Tataru-Tohaneanu in a liner setting and is also related to Alinhac’s ghost weight method. This is a joint work with M. Ifrim.

Almost-Global Well-Posedness for 2d Strongly-Coupled Wave-Klein-Gordon Systems