Strichartz Estimates for Water Waves

Understanding the well-posedness of nonlinear evolution equations for low regularity data is a fundamental question in the analysis of PDEs. In the context of dispersive evolution equations, including the water waves equations, various estimates that arise as a consequence of dispersion serve as tools which can extend well-posedness to lower regularity data than that which can be proven using energy estimates alone. In particular, a class of dispersive estimates known as Strichartz estimates play an important role in the low regularity theory.