BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Knots and links in fluid mechanics - Enciso\, A (I
nstituto de Ciencias Matemticas\; Madrid)
DTSTART;TZID=Europe/London:20120724T094500
DTEND;TZID=Europe/London:20120724T100500
UID:TALK39027AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/39027
DESCRIPTION:In this talk I will discuss the existence of stead
y solutions to the incompressible Euler equations
that have stream and vortex lines of any prescribe
d knot (or link) type. More precisely\, I will sho
w that\, given any locally finite link L in R^3\,
one can transform it by a smooth diffeomorphism F\
, close to the identity in any C^p norm\, such tha
t F(L) is a set of periodic trajectories of a real
analytic steady solution u of the Euler equations
in R^3. If the link is finite\, we shall also see
that u can be assumed to decay as 1/|x| at infini
ty\, so that u is in L^p for all p>3. This problem
is motivated by the well-known analysis of the st
ructure of steady incompressible flows due to V.I.
Arnold and K. Moffatt\, among others. \n\nTime pe
rmitting\, we will also very recent results on the
topology of potential flows\, that is\, of steady
fluids whose velocity field is the gradient of a
harmonic function in R^3. These results are closel
y related to classic questions in potential theory
that were first considered by M. Morse and W. Kap
lan in the first half of the XX century and have b
een revisited several times after that\, by Rubel\
, Shiota and others. \n\nThe guiding principle of
the talk will be that a strategy of "local\, analy
sis-based constructions" + "global approximation m
ethods"\, fitted together using ideas from differe
ntial topology\, can be used to shed some light on
the qualitative behavior of steady fluid flows. M
ost of the original results presented in this talk
will be based on the papers: \n\nA. Enciso\, D. P
eralta-Salas\, Knots and links in steady solutions
of the Euler equation\, Ann. of Math. 175 (2012)
345-367. \n\nA. Enciso\, D. Peralta-Salas\, Subman
ifolds that are level sets of solutions to a secon
d-order elliptic PDE\, arXiv:1007.5181. \n\nA. Enc
iso\, D. Peralta-Salas\, Arnold's structure theore
m revisited\, in preparation.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
END:VEVENT
END:VCALENDAR