Global Strong Solutions for the Two-Dimensional Motion of an Infinite Cylinder in a Viscous Fluid

Abstract

In this paper, we consider a two-dimensional fluid-rigid body problem. The motion of the fluid is modelled by the Navier-Stokes equations, whereas the dynamics of the rigid body is governed by the conservation laws of linear and angular momentum. The rigid body is supposed to be an infinite cylinder of circular cross-section. Our main result is the existence and uniqueness of global strong solutions. Mathematics Subject Classification (2000). 35Q30, 76D03, 76D05.

Existence of Weak Solutions for the Unsteady Interaction of a Viscous Fluid with an Elastic Plate

“…In most of the previous studies the structure velocity is quite regular because of the model or because of the presence of a regularization operator in the equations. The existing results are concerned mainly with rigid body motions [5], [10], [11], [13], [16], [17], [18], [21], [22], [25], [24] or with the motion of a structure described by a finite number of modal functions [12] or a structure with additional "viscous" terms [2], [4], [8]. Recently, a significant breakthrough has been made by D. Coutand and S. Shkoller.…”

Well posedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid

“…However, as far as we know, only few results concerning the existence and uniqueness of strong solutions for the problem (1.1), (1.2), (1.4)-(1.10) are available in the case where the system fills the whole space. In that case, we can mention the results of Takahashi and Tucsnak [22], and of Galdi and Silvestre [9]. In [22], the authors show the global in time existence and uniqueness of strong solutions in two spatial dimensions in the particular case where the rigid body is a disk.…”

“…In that case, we can mention the results of Takahashi and Tucsnak [22], and of Galdi and Silvestre [9]. In [22], the authors show the global in time existence and uniqueness of strong solutions in two spatial dimensions in the particular case where the rigid body is a disk. In [9], the authors prove the existence of local in time strong solutions for a rigid body having an arbitrary regular shape.…”

“…The existence of solutions for the problem (1.1), (1.2), (1.4)-(1.10), with initial data satisfying the same assumptions as in Theorem 1.1 has already been investigated in [22] assuming that the rigid body is an infinite cylinder of circular cross-section. Moreover, a similar problem was studied in [9], where the difference with our problem is that in [9], the authors suppose that there are prescribed external forces and torques acting on the rigid body and assume that only conservative forces act on the fluid.…”

Classical solutions for the equations modelling the motion of a ball in a bidimensional incompressible perfect fluid

“…These difficulties occur in any fluid-structure problem. In the last decade, several papers have been devoted to the existence of solutions for such systems when the fluid motion is governed by Navier-Stokes equations; to quote a few, Desjardins and Esteban [5,6], Conca, San Martín and Tucsnak [2], Gunzburger, Lee and Seregin [16], Hoffmann and Starovoitov [18,19], Grandmont and Maday [15], San Martín, Starovoitov and Tucsnak [26], Feireisl [7][8][9], Takahashi [30] (in the case of a bounded domain) and Serre [27], Judakov [20], Silvestre [28], Takahashi-Tucsnak [31], Galdi and Silvestre [11] (in the case where the fluid-rigid body system fills the whole space). The stationary problem was studied in Serre [27] and in Galdi [10].…”