题目: Long time behavior of the 3D water waves system in the finite depth setting
摘要: In this talk, we will mainly discuss the small data global regularity problem for the 3D gravity waves system and the 3D capillary waves system in the finite depth setting. If the initial data is smooth, well localized, and suitably small, we show that there exists a unique global solution. Moreover, the global solution possesses the scattering property. As a byproduct, we also know the nonexistence of small (in $L^2$ sense) traveling waves.