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 s>7/10 in the radial case and down to s>13/18 in the general case.