BEGIN:VCALENDAR
VERSION:2.0
CALSCALE:GREGORIAN
PRODID:iCalendar-Ruby
BEGIN:VEVENT
CATEGORIES:Lecture / Talk / Workshop
DESCRIPTION:Alexis Vasseur\, University of Texas Austin\n\nAbstract: Consid
er the steady solution to the incompressible Euler equation $Ae_1$ in the p
eriodic tunnel $\Omega=[0\,1]\times \mathbb T^2$. Consider now the family o
f solutions $U_\nu$ to the associated Navier-Stokes equation with no-slip c
ondition on the flat boundaries\, for small viscosities $\nu=1/ Re$\, and i
nitial values close in $L^2$ to $Ae_1$. Under a conditional assumption on t
he energy dissipation close to the boundary\, Kato showed in 1984 that $U
_\nu$ converges to $Ae_1$ when the viscosity converges to 0 and the initial
value converge to $A e_1$. It is still unknown whether this inviscid is u
nconditionally true. Actually\, the convex integration method predicts the
possibility of a layer separation. It produces solutions to the Euler equat
ion with initial values $Ae_1 $\, but with layer separation energy at tim
e T up to: $$\|U(T)-Ae_1\|^2_{L^2}\equiv A^3T.$$\nIn this work we prove th
at at the double limit for the inviscid asymptotic $\bar{U}$\, where both
the Reynolds number $Re$ converges to infinity and the initial value $U_{\n
u}$ converges to $Ae_1$ in $L^2$\, the energy of layer separation cannot be
more than:\n$$\| \bar{U}(T)-Ae_1\|^2_{L^2}\lesssim A^3T.$$ Especially\, it
shows that\, even if if the limit is not unique\, the shear flow pattern i
s observable up to time $1/A$. This provides a notion of stability despite
the possible non-uniqueness of the limit predicted by the convex integratio
n theory. The result relies on a new boundary vorticity estimate for the Na
vier-Stokes equation. This new estimate\, inspired by previous work on high
er regularity estimates for Navier-Stokes\, provides a non-linear control s
calable through the inviscid limit.
DTEND:20220208T003000Z
DTSTAMP:20241103T170230Z
DTSTART:20220207T233000Z
LOCATION:
SEQUENCE:0
SUMMARY:CAMS Colloquium: Boundary vorticity estimate for the Navier-Stokes
equation and control of layer separation in the inviscid limit
UID:tag:localist.com\,2008:EventInstance_38944195996718
URL:https://calendar.usc.edu/event/cams_colloquium_boundary_vorticity_estim
ate_for_the_navier-stokes_equation_and_control_of_layer_separation_in_the_i
nviscid_limit
END:VEVENT
END:VCALENDAR