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BEGIN:VEVENT
UID:61f2172e41fdb
DTSTART:20211029T140000Z
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DTEND:20211029T150000Z
URL:https://www.imperial.ac.uk/events/139216/helmut-abels/
LOCATION:United Kingdom
SUMMARY:Helmut Abels: On the sharp interface limit of a Navier-Stokes/Allen
-Cahn system
CLASS:PUBLIC
DESCRIPTION:We consider the sharp interface limit of a Navier-Stokes/Allen-
Cahn system\, when a parameter $\\varepsilon>0$ that is proportional to th
e thickness of the diffuse interface tends to zero\, in a two dimensional
bounded domain. We present a recent result in which we prove convergence f
or sufficiently small times of the solutions of the Navier-Stokes/Allen-Ca
hn system to solutions of a sharp interface model\, where the interface ev
olution is given by the mean curvature equation with an additional convect
ion term coupled to a two-phase Navier-Stokes system with an additional co
ntribution to the stress tensor\, which describes the capillary stress. To
this end we construct a suitable approximation of the solution of the Nav
ier-Stokes/Allen-Cahn system. To this end a new Ansatz based on partial li
nearization in highest order is used\, which simplifies the analysis compa
red to previous results. Then the difference of approximate and exact solu
tion is estimated with the aid of a suitable spectral estimate of the line
arized Allen-Cahn operator. This is a joint work with Mingwen Fei from Anh
ui Normal University\, China.
X-ALT-DESC;FMTTYPE=text/html:We consider the sharp interface limit of a
Navier-Stokes/Allen-Cahn system\, when a parameter $\\varepsilon>0$ that i
s proportional to the thickness of the diffuse interface tends to zero\, i
n a two dimensional bounded domain. We present a recent result in which we
prove convergence for sufficiently small times of the solutions of the Na
vier-Stokes/Allen-Cahn system to solutions of a sharp interface model\, wh
ere the interface evolution is given by the mean curvature equation with a
n additional convection term coupled to a two-phase Navier-Stokes system w
ith an additional contribution to the stress tensor\, which describes the
capillary stress. To this end we construct a suitable approximation of the
solution of the Navier-Stokes/Allen-Cahn system. To this end a new Ansatz
based on partial linearization in highest order is used\, which simplifie
s the analysis compared to previous results. Then the difference of approx
imate and exact solution is estimated with the aid of a suitable spectral
estimate of the linearized Allen-Cahn operator. This is a joint work with
Mingwen Fei from Anhui Normal University\, China.

DTSTAMP:20220127T035318Z
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