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


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 Rondianski. 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 two results, in collaboration with Shijie Dong (Fudan), where we investigate the small data global-existence of semilinear wave-Klein-Gordon equations in two and three spatial dimensions.

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