Urbana Campus Research Calendar (OVCRI)

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Capillary gravity water waves linearized at monotone shear flows: eigenvalues and inviscid damping

Event Type
Seminar/Symposium
Sponsor
Department of Mathematics
Location
243 Altgeld Hall
Date
Feb 21, 2023   1:00 - 2:00 pm  
Speaker
Xiao Liu
Views
22
Originating Calendar
Harmonic Analysis and Differential Equations Seminar (HADES)

We consider the 2-dim capillary gravity water wave problem -- the free boundary problem of the Euler equation with gravity and surface tension -- of finite depth $x_2 \in (-h, 0)$ linearized at a uniformly monotonic shear flow $U(x_2)$. We provide a complete picture of the eigenvalue distribution and prove the linear inviscid damping near monotone shear flow under some certain conditions. This is a joint work with Chongchun Zeng.

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