Advances in Differential Equations

Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain

Takéo Takahashi

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Abstract

In this paper, we study a fluid--rigid-body interaction problem. The motion of the fluid is modeled by the Navier-Stokes equations, written in an unknown bounded domain depending on the displacement of the rigid body. Our main result yields existence and uniqueness of strong solutions. In the two-dimensional case, the solutions are global provided that the rigid body does not touch the boundary. In the three-dimensional case, we obtain local-in-time existence and global existence for small data. Moreover, we prove an asymptotic stability result.

Article information

Source
Adv. Differential Equations Volume 8, Number 12 (2003), 1499-1532.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867983

Mathematical Reviews number (MathSciNet)
MR2029294

Zentralblatt MATH identifier
1101.35356

Subjects
Primary: 76D03: Existence, uniqueness, and regularity theory [See also 35Q30]
Secondary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D05: Navier-Stokes equations [See also 35Q30]

Citation

Takahashi, Takéo. Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain. Adv. Differential Equations 8 (2003), no. 12, 1499--1532. https://projecteuclid.org/euclid.ade/1355867983.


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