## IMA Postdoc Seminar (February 3, 2009)

**Speaker:** Wei Xiong (IMA)

**Title:** Hydrodynamics of particles immersed in a thermally
fluctuating, viscous, incompressible fluid

**Abstract:** My current work concerns the hydrodynamics of particles immersed in a
thermally fluctuating, viscous, incompressible fluid. The governing
equations stipulate conservation of momentum in the fluid, conservation
of linear and angular momentum of the particle, and no-slip boundary
conditions on the boundary of the particle. Is there existence and
uniqueness for the solution? What are the limit theorems when time goes
to infinity? These problems not only provide more detailed study of
physical Brownian motions but also give a testing ground for the
techniques in stochastic partial differential equations.

In this talk, I will focus on particles passively advected by the fluid.
I will give existence and uniqueness results for passive particles
(point particles as well as finite size particles) immersed in the
fluid, and I will give limit theorems when the time goes to infinity.
Also, I will give numerical simulations of the motion of the particle
in the case of deterministic forcing, and a numerical scheme for the
stochastic forcing case.