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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Wave patterns beneath an ice cover - Andrej Ilâ€™ich
ev (Steklov Mathematical Institute\, Russian Acade
my of Sciences )
DTSTART;TZID=Europe/London:20171003T161500
DTEND;TZID=Europe/London:20171003T170000
UID:TALK87411AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/87411
DESCRIPTION:We prove existence of the soliton-like solutions o
f the full system of equations which describe wave
propagation in the fluid of a finite depth under
an ice cover. These solutions correspond to solita
ry waves of various nature propagating along the w
ater-ice interface. We consider the plane-parallel
movement in a layer of the perfect fluid of the f
inite depth which characteristics obey the full 2D
Euler system of equations. The ice cover is model
ed by the elastic Kirchgoff-Love plate and it has
a considerable thickness so that the plate inertia
is taken into consideration when the model is for
mulated. The Euler equations contain the additiona
l pressure arising from the presence of the elasti
c plate freely floating on the liquid surface. The
mentioned families of the solitary waves are para
meterized by a speed of the wave and their existen
ce is proved for the speeds lying in some neighbor
hood of its critical value corresponding to the qu
iescent state. S olitary waves\, in their turn\, b
ifurcate from the quiescent state and lie in some
neighborhood of it. By other words\, existence of
solitary waves of sufficiently small amplitudes on
the water-ice interface is proved. The proof is c
onducted with the help of the projection of the re
quired system to the central manifold and further
analysis of the resulting reduced finite dimension
al dynamical system on the central manifold.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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