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math.AP2024
On the capillary water waves with constant vorticity
Lizhe Wan
This article is devoted to the study of local well-posedness for deep water waves with constant vorticity in two space dimensions on the real line. The water waves can be paralinea…
math.AP2024
Low regularity well-posedness for two-dimensional deep water waves
Lizhe Wan
The study of gravity-capillary water waves in two space dimensions has been an important question in mathematical fluid dynamics. By implementing the cubic modified energy method o…
math.AP2024★ 1 cited
Two-dimensional solitary water waves with constant vorticity, Part II: the deep capillary case
James Rowan, Lizhe Wan
We consider the two-dimensional capillary water waves with nonzero constant vorticity in infinite depth. We first derive the Babenko equation that describes the profile of the soli…