Global analysis of the defocusing cubic wave equation in dimension 3

The local existence of solutions of semilinear wave equations is now understood. But the long-time behavior of these solutions is still poorly understood. In this thesis, we study the global existence of solutions of the defocusing cubic wave equation in three dimensions. We prove that the solutions exist globally in time with rougher data than those in the existing literature. In particular, we prove global well-posedness down to s7/10 in the radial case and down to s13/18 in the general case.

Autorentext

Doctor Tristan Roy got a PhD degree in mathematics in 2008 from University of California, Los Angeles, USA, under the direction of Prof Terence Tao. His area of expertise is the long-time behavior of solutions of semilinear dispersive equations.