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# Zoe Wyatt, Cambridge – Analysis & PDE Seminar

## October 27, 2021 @ 12:00 pm - 1:00 pm

Virtual and alternative time to be arranged to accommodate time difference

Meeting in-person, 12:00 – 1:00 pm in Phillips Hall 228

**Title:** Coupled wave and Klein-Gordon equations in two and three spatial dimensions

**Abstract:** Semilinear wave equations in three spatial dimensions with wave–wave nonlinearities exhibit interesting and well-studied phenomena: from John’s famous blow-up examples, to the null condition of Christodoulou and Klainerman, and more recently to the weak null condition of Lindblad and Rodnianski. The study of coupled semilinear wave and Klein-Gordon equations is less well-developed, and interesting problems occur across the possible spectrum of wave–wave, wave–KG and KG–KG interactions. In this talk I will discuss some recent results, in collaboration with Shijie Dong (Fudan), on such mixed systems. This includes a recent proof of small data global-existence and sharp asymptotics for a Dirac–Klein-Gordon system in two spatial dimensions.