Asymptotic analysis of the system describing a small moving rigid body in viscous incompressible fluid

Abstract: We consider the interaction between a viscous incompressible fluid and a small rigid body, which is immersed in the fluid. The fluid is modeled by the 3D Navier-Stokes equations. The motion of the body obeys the conservation of linear and angular momentum. We assume that the density of the body is constant which is independent of the size of the body ε. Based on the L p − L q estimate of the so-called fluid-structure semigroup, we obtain a uniform estimate for the velocity of the body. In particular, we show that these estimates are ε-invariant. This help us to construct an approximation sequence of the test functions of the fluid-body system. We prove that the solution of the fluid-body system, in appropriate sense, converges to a solution of the Navier-Stokes equations as ε → 0. This is a joint work with Jiao He (Univerist´e Paris-Sud).

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)