Long-time behavior for the two-dimensional motion of a disk in a viscous fluid

Lacave, Christophe; Hillairet, Matthieu; Ervedoza, Sylvain

Lacave, Christophe; Hillairet, Matthieu; Ervedoza, Sylvain (2014), Long-time behavior for the two-dimensional motion of a disk in a viscous fluid, Communications in Mathematical Physics, 329, 1, p. 325-382. http://dx.doi.org/10.1007/s00220-014-1884-5

Type

Article accepté pour publication ou publié

External document link

http://fr.arxiv.org/abs/1301.4420

Date

2014

Journal name

Communications in Mathematical Physics

Volume

329

Number

Publisher

Springer

Pages

325-382

Abstract (EN)

In this article, we study the long-time behavior of solutions of the two-dimensional fluid-rigid disk problem. The motion of the fluid is modeled by the two-dimensional Navier-Stokes equations, and the disk moves under the influence of the forces exerted by the viscous fluid. We first derive $L^p$-$L^q$ decay estimates for the linearized equations and compute the first term in the asymptotic expansion of the solutions of the linearized equations. We then apply these computations to derive time-decay estimates for the solutions to the full Navier-Stokes fluid-rigid disk system.

Subjects / Keywords

viscosity; fluid-rigid disk system; Navier-Stokes equations