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DTSTART:20240412T210000Z
UID:179171@events.unl.edu
DTSTAMP:20240210T215724Z
ORGANIZER;CN=Kazuo Yamazaki:
SUMMARY:Kazuo Kamakazi\, University of Nebraska - Lincoln
STATUS:CONFIRMED
DESCRIPTION:In the first half\, I will describe recent breakthroughs in the
research direction of singular stochastic PDEs that appear frequently in
mathematical physics. In the second half\, I will describe another recent
breakthrough technique of convex integration in hydrodynamics and its cons
equence on turbulence.\n\nFirst\, many equations in mathematical physics w
ere suggested in the form of PDEs with random force\, specifically the so-
called space-time white noise\, e.g.\, the Kardar-Parisi-Zhang equation in
1986. Due to the singularity of the noise\, the solution turns out to be
a distribution rather than a function leading to the nonlinear term within
the PDE to be ill-defined. Breakthrough techniques of the theory of regul
arity structures by Hairer and the theory of paracontrolled distributions
by Gubinelli\, Imkeller\, and Perkowski now allow us to understand its (ve
ry weak) solution theory.\n\nSecond\, turbulence occurs in our daily lives
. E.g.\, in airplanes\, we are all reminded by flight attendants to keep o
ur seatbelts fastened in preparation for “unexpected turbulence”. Kolm
ogorov’s zeroth law of turbulence from 1941 was supported by numerical a
nalysis under the name of “anomalous dissipation”. Closely related are
the famous Onsager’s conjecture in 1949 and Taylor’s conjecture in 19
74. It is only in the last decade that the breakthrough technique of conve
x integration finally led to mathematically rigorous resolutions to such c
onjectures.
LOCATION:Avery Hall Room 115
URL://events.unl.edu/Nebraska_Unions/2024/04/12/179171/
DTEND:20240412T220000Z
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