PDE Real Analysis Seminar

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

2011/04/20

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Yoshida, Nobuo (Department of Mathematics, Kyoto University)
Stochastic power law fluids (JAPANESE)
[ Abstract ]
This talk is based in part on a joint work with Yutaka Terasawa.
We consider a SPDE (stochastic partial differential equation) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force.
Here, the extra stress tensor of the fluid is given by a polynomial of degree $p-1$ of the rate of strain tensor, while the colored noise is considered as a random force.
We first investigate the existence and the uniqueness of weak solutions to this SPDE.
We next turn to the special case: $p \\in [1 + {d \\over 2},{2d\\overd-2})$,
where $d$ is the dimension of the space. We prove there that the Galerkin scheme approximates the velocity field in a strong sense. As a consequence, we establish the energy equality for the velocity field.
[ Reference URL ]
http://www.math.kyoto-u.ac.jp/~nobuo/