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Nonlinear wave equations on time dependent inhomogeneous backgrounds

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In this talk, I will talk about the nonlinear wave equations on a class of asymptotically flat Lorentzian manifolds ({R}^{3+1}, g) with time dependent inhomogeneous metric g. Based on a new approach for proving the decay of solutions of linear wave equations, we give several applications to nonlinear problems. In particular, we will show the small data global existence result for quasilinear wave equations satisfying the null condition on a class of time dependent inhomogeneous backgrounds which do not settle to any particular stationary metric.

This talk is part of the Cambridge Analysts' Knowledge Exchange (C.A.K.E.) series.

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