Long-Time Behavior for the Two-Dimensional Motion of a Disk in a Viscous Fluid

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...

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Bibliographic Details
Published in:Communications in mathematical physics 2014-07, Vol.329 (1), p.325-382
Main Authors: Ervedoza, S., Hillairet, M., Lacave, C.
Format: Article
Language:English
Subjects:
Analysis of PDEs
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Mathematics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-014-1884-5