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

Abstract : 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.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-00778849
Contributor : Christophe Lacave Connect in order to contact the contributor
Submitted on : Monday, January 21, 2013 - 3:04:50 PM
Last modification on : Monday, July 4, 2022 - 10:22:30 AM

### Citation

Sylvain Ervedoza, Matthieu Hillairet, Christophe Lacave. Long-time behavior for the two-dimensional motion of a disk in a viscous fluid. Communications in Mathematical Physics, Springer Verlag, 2014, 329 (1), pp.325-382. ⟨10.1007/s00220-014-1884-5⟩. ⟨hal-00778849⟩

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