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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On the fully nonlinear 2D Peskin problem - Robert
Strain (University of Pennsylvania)
DTSTART;TZID=Europe/London:20220113T160000
DTEND;TZID=Europe/London:20220113T170000
UID:TALK166702AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/166702
DESCRIPTION:The Peskin problem models the dynamics of a closed
elastic string immersed in an incompressible 2D s
tokes fluid. This set of equations was proposed as
a simplified model to study blood flow through he
art valves. The immersed boundary formulation of t
his problem has proven very useful in particular g
iving rise to the widely used immersed boundary me
thod in numerical analysis. Proving the existence
and uniqueness of smooth solutions is vitally usef
ul for this system in particular to guarantee that
numerical methods based upon different formulatio
ns of the problem all converge to the same solutio
n. In this project ``Critical local well-posedness
for the fully nonlinear Peskin problem''\, which
is a joint work with Stephen Cameron\, we consider
the case with equal viscosities but with a fully
non-linear tension law. This situation has been ca
lled the fully nonlinear Peskin problem. In this c
ase we prove local wellposedness for arbitrary ini
tial data in the scaling critical Besov space $\\d
ot{B}^{3/2}_{2\,1}(\\mathbb{T}\; \\mathbb{R}^2)$.
We additionally prove the high order smoothing eff
ects for the solution. To prove this result we der
ive a new formulation of the equation that describ
es the parametrization of the string\, and we cruc
ially utilize a new cancellation structure.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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