PDE Real Analysis Seminar

Seminar information archive ~03/19Next seminarFuture seminars 03/20~

Date, time & place Tuesday 10:30 - 11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

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10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Tatsu-Hiko Miura (The University of Tokyo)
Global existence of a strong solution to the Navier-Stokes equations in a curved thin domain (Japanese)
[ Abstract ]
In this talk, we consider the Navier-Stokes equations with Navier's slip boundary conditions in a three-dimensional curved thin domain around a closed surface.
We establish the global-in-time existence of a strong solution for large data when the width of the thin domain is very small.
A key idea is to decompose a three-dimensional vector field into the average part which is almost two-dimensional and the residual part to which we can apply Poincaré type inequalities.
Such decomposition enables us to derive a good estimate for the inner product of the inertia term and the viscous term, which is essential for our arguments.