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SUMMARY:Walter Strauss (Brown University)
DTSTART;VALUE=DATE-TIME:20200915T190000Z
DTEND;VALUE=DATE-TIME:20200915T200000Z
DTSTAMP;VALUE=DATE-TIME:20201031T052812Z
UID:ONEPAS/1
DESCRIPTION:Title: Introduction to steady water waves\nby Walter Strauss (
Brown University) as part of Online Northeast PDE and Analysis Seminar\n\n
\nAbstract\nThis is a very basic introduction. No previous knowledge of w
ater waves is required. I will mention the high points of the history of w
ater wave theory. Then the fundamental equations inside the water and on
the free boundary will be discussed. Finally\, many important directions o
f current research will be briefly outlined.\n
END:VEVENT
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SUMMARY:John Toland (University of Bath)
DTSTART;VALUE=DATE-TIME:20200922T190000Z
DTEND;VALUE=DATE-TIME:20200922T200000Z
DTSTAMP;VALUE=DATE-TIME:20201031T052812Z
UID:ONEPAS/2
DESCRIPTION:Title: Variational aspects of steady irrotational water wave t
heory\nby John Toland (University of Bath) as part of Online Northeast PDE
and Analysis Seminar\n\n\nAbstract\nAmong the many modern approaches to a
bstract nonlinear problems\, those based on the implicit function theorem\
, real-analytic function theory\, Nash-Moser theory and topological degree
theory have made significant contributions to water-wave theory in recent
years. However\, the same cannot be said of variational methods (min/max\
, mountain-pass\, Morse index\, Lyusternik-Schnirelman genus etc) even tho
ugh\, when the viscosity of water is ignored and the flow is assumed to be
irrotational\, there are several attractive ways to formulate the equatio
ns of wave motion variationally. On the 100th anniversary of the first pro
of that the equations of motion have non-zero\, small-amplitude solutions\
, this talk will briefly survey these issues and advocate variational meth
ods for analyzing water waves that are 2π-periodic in space.\n
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BEGIN:VEVENT
SUMMARY:Susanna Haziot (University of Vienna)
DTSTART;VALUE=DATE-TIME:20200929T190000Z
DTEND;VALUE=DATE-TIME:20200929T200000Z
DTSTAMP;VALUE=DATE-TIME:20201031T052812Z
UID:ONEPAS/3
DESCRIPTION:Title: Rotational water waves\nby Susanna Haziot (University o
f Vienna) as part of Online Northeast PDE and Analysis Seminar\n\n\nAbstra
ct\nOne significant difficulty of working with water waves is that the bou
ndary of the fluid domain itself is an unknown. I will begin with a brief
presentation of the steady water wave problem for waves with vorticity. Su
bsequently\, I will review some existence results as well as present recen
t research which involve different methods for transforming the fluid doma
in into a fixed domain.\n
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SUMMARY:Vera Mikyoung Hur (University of Illinois at Urbana-Champaign)
DTSTART;VALUE=DATE-TIME:20201013T190000Z
DTEND;VALUE=DATE-TIME:20201013T200000Z
DTSTAMP;VALUE=DATE-TIME:20201031T052812Z
UID:ONEPAS/4
DESCRIPTION:Title: Stokes waves in constant vorticity flows\nby Vera Mikyo
ung Hur (University of Illinois at Urbana-Champaign) as part of Online Nor
theast PDE and Analysis Seminar\n\n\nAbstract\nI will discuss recent progr
ess on the numerical computation of Stokes waves in constant vorticity flo
ws. Based on a Babenko-kind equation\, our result improves those in the 19
80s by Simmen and Saffman\, Teles da Silva and Peregrine. Notably\, it rev
eals a plethora of new solutions: Crapper's exact solution (even though th
ere is no surface tension)\, a fluid disk in rigid body rotation\, etc. I
will also discuss the effects of vorticity on the extreme wave\, particula
rly\, the maximum slope for an almost extreme wave. I will discuss some op
en problems\, both analytical and numerical.\n
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BEGIN:VEVENT
SUMMARY:Samuel Walsh (University of Missouri)
DTSTART;VALUE=DATE-TIME:20201027T190000Z
DTEND;VALUE=DATE-TIME:20201027T200000Z
DTSTAMP;VALUE=DATE-TIME:20201031T052812Z
UID:ONEPAS/5
DESCRIPTION:Title: Water waves with density stratification or localized vo
rticity\nby Samuel Walsh (University of Missouri) as part of Online Northe
ast PDE and Analysis Seminar\n\n\nAbstract\nThis talk will serve as a gene
ral introduction to two areas of active research in water waves. In the oc
ean\, the presence of salt and temperature gradients can lead to substanti
al stratification of the density. This phenomenon is well-known to have si
gnificant physical implications. Indeed\, it makes possible enormous ``int
ernal waves'' that can dwarf even the largest waves seen on the surface. W
e will present an overview of the mathematical work on this subject\, focu
sing primarily on recent results regarding the existence of large-amplitud
e solitary stratified waves.\n\nThe second part of the talk will discuss w
aves with localized distributions of vorticity. These include water waves
with submerged point vortices\, dipoles\, vortex patches\, and those exhib
iting a vortex spike.\n\nThis is joint work with Robin Ming Chen\, Mats Eh
rnström\, Jalal Shatah\, Kristoffer Varholm\, Erik Wahlén\, Miles H. Wh
eeler\, and Chongchun Zeng.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miles Wheeler (University of Bath)
DTSTART;VALUE=DATE-TIME:20201020T190000Z
DTEND;VALUE=DATE-TIME:20201020T200000Z
DTSTAMP;VALUE=DATE-TIME:20201031T052812Z
UID:ONEPAS/6
DESCRIPTION:Title: Solitary waves and fronts\nby Miles Wheeler (University
of Bath) as part of Online Northeast PDE and Analysis Seminar\n\n\nAbstra
ct\nI will give a general introduction to the theory of solitary water wav
es\, that is traveling waves whose surfaces converge to some asymptotic he
ight at infinity. In many respects\, the theory for solitary waves is more
difficult and more subtle than that for periodic waves. Yet in other ways
the problem is much simpler\, and indeed many results for solitary waves
are stronger than their periodic counterparts. \n\nBeginning with the line
ar theory\, or perhaps more accurately the *lack* of a linear theor
y\, I will explain how small-amplitude waves can be rigorously constructed
via a center manifold reduction. Next I will collect a series of results
which together guarantee that any solitary wave\, regardless of amplitude\
, is symmetric and decreasing about a central crest and travels at a “su
percritical” speed $c>\\sqrt{gd}$. Finally\, I will explain how the sign
ificant obstacles to applying global bifurcation techniques can be overcom
e by taking advantage of the above properties together with the *nonexi
stence* of front-type solutions. This approach is surprisingly robust\
, and has recently been generalized to apply to front-type solutions in ad
dition to solitary waves.\n
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SUMMARY:Erik Wahlén (Lund University)
DTSTART;VALUE=DATE-TIME:20201103T200000Z
DTEND;VALUE=DATE-TIME:20201103T210000Z
DTSTAMP;VALUE=DATE-TIME:20201031T052812Z
UID:ONEPAS/7
DESCRIPTION:Title: Three-dimensional water waves\nby Erik Wahlén (Lund Un
iversity) as part of Online Northeast PDE and Analysis Seminar\n\n\nAbstra
ct\nThe other talks in the series have concentrated on two-dimensional wat
er waves. In my talk I will give an overview of the considerably younger t
hree-dimensional theory. In the irrotational case\, there is by now a rich
existence theory for small-amplitude solutions. These can have different
behaviours in different horizontal directions\, e.g. periodic or solitary.
In the talk I will mainly focus on waves which are "doubly periodic"\, th
at is\, periodic in two different horizontal directions\, or "fully locali
sed"\, that is\, solitary in all horizontal directions. As we will see\, s
urface tension plays a much more crucial role than in 2D. I will also disc
uss some recent work on 3D water waves with vorticity.\n
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