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SUMMARY:Upper bound on the slope of a steady water wave - Walter Strauss (
 Brown University)
DTSTART:20170810T103000Z
DTEND:20170810T113000Z
UID:TALK75341@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Consider the angle of inclination of the profile of a steady 2
 D (inviscid\,&nbsp\; symmetric\, periodic or solitary) water wave subject 
 to gravity. Although&nbsp\; the angle may surpass 30 degrees for some irro
 tational waves close to the&nbsp\; extreme Stokes wave\, Amick proved in 1
 987 that the angle must be less than&nbsp\; 31.15 degrees if the wave is i
 rrotational.&nbsp\; However\, for any wave that is&nbsp\; not irrotational
 \, the question of whether there is any bound on the angle&nbsp\; has been
  completely open. An example is the extreme Gerstner wave\, which&nbsp\; h
 as adverse vorticity and vertical cusps. Moreover\, numerical calculations
 &nbsp\; show that waves of finite depth with adverse vorticity can overtur
 n\,&nbsp\; so the angle can be 90 degrees.&nbsp\; On the other hand\, Mile
 s Wheeler and I&nbsp\; prove that there is an upper bound of 45 degrees fo
 r a large class of&nbsp\; waves with favorable vorticity and finite depth.
 &nbsp\; Seung Wook So and I&nbsp\; prove a similar bound for waves with sm
 all adverse vorticity. &nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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