As a starting point for studying the long-time behavior of the 3-dimensional water waves system in the flat bottom setting, we try to improve the understanding of the Dirichlet–Neumann operator in this set-up. As an application, we study the 3-dimensional gravity waves system and derive a new energy estimate of type, which has good structure in the -type space. This has been used in our Ph.D. thesis (2016) to prove the global regularity of the 3-dimensional gravity waves system for suitably small initial data.
"On the 3-dimensional water waves system above a flat bottom." Anal. PDE 10 (4) 893 - 928, 2017. https://doi.org/10.2140/apde.2017.10.893