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BEGIN:VEVENT
UID:428b5586687276589cc21a1e3be03a1f
CATEGORIES:Nonlinear Analysis
CREATED:20241008T215411
SUMMARY:Chongchun Zeng:   Water waves linearized at monotonic shear flows
LOCATION:Hill 705
DESCRIPTION:Abstract: We consider the 2-dim water wave problem -- the free boundary pro
 blem of the Euler equation with gravity and possibly surface tension -- of 
 finite depth linearized at a uniformly monotonic shear flow $U(x_2)$. Our m
 ain focuses are eigenvalue distribution and inviscid damping. We first prov
 e that in contrast to finite channel flow and gravity waves, the linearized
  capillary gravity wave has two unbounded branches of eigenvalues for high 
 wave numbers. They may bifurcate into unstable eigenvalues through a rather
  degenerate bifurcation. Under certain conditions, we provide a complete pi
 cture of the eigenvalue distribution. Assuming there are no singular modes 
 (i.e. embedded eigenvalues), we obtain the linear inviscid damping. We also
  identify the leading asymptotic terms of velocity and obtain stronger deca
 y for the remainders. The linearized gravity waves will also be discussed b
 riefly if time permits. This is a joint work with Xiao Liu.\n
X-ALT-DESC;FMTTYPE=text/html:<p style="color: #000000; font-family: -webkit-standard; font-weight: 400; 
 letter-spacing: normal; text-align: left; text-indent: 0px; text-transform:
  none; white-space: normal; word-spacing: 0px; text-decoration: none;"><str
 ong>Abstract:&nbsp;</strong>We consider the 2-dim water wave problem -- the
  free boundary problem of the Euler equation with gravity and possibly surf
 ace tension -- of finite depth linearized at a uniformly monotonic shear fl
 ow $U(x_2)$. Our main focuses are eigenvalue distribution and inviscid damp
 ing. We first prove that in contrast to finite channel flow and gravity wav
 es, the linearized capillary gravity wave has two unbounded branches of eig
 envalues for high wave numbers. They may bifurcate into unstable eigenvalue
 s through a rather degenerate bifurcation. Under certain conditions, we pro
 vide a complete picture of the eigenvalue distribution. Assuming there are 
 no singular modes (i.e. embedded eigenvalues), we obtain the linear invisci
 d damping. We also identify the leading asymptotic terms of velocity and ob
 tain stronger decay for the remainders. The linearized gravity waves will a
 lso be discussed briefly if time permits. This is a joint work with Xiao Li
 u.</p>
CONTACT:Georgia Institute of Technology
DTSTAMP:20260829T233331
DTSTART;TZID=America/New_York:20241202T103000
DTEND;TZID=America/New_York:20241202T113000
SEQUENCE:0
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