On the stability of a top with a cavity filled with a viscous fluid

Kostyuchenko, A. G.; Шкаликов, А. А.; Yurkin, M. Yu.

doi:10.1007/bf02482596

Cited by 16 publications

(17 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our other main objective in this section is to show necessary and sufficient conditions for stability for the full nonlinear problem, without any approximation. These conditions contain those of [20] as a particular case, and extend those of [13,3,22] to the nonlinear level.…”

mentioning

confidence: 88%

Inertial motions of a rigid body with a cavity filled with a viscous liquid

Galdi

Mazzone

Zunino

2013

Comptes Rendus. Mécanique

View full text Add to dashboard Cite

In this note we announce a number of analytical and numerical results related to the motion of a system S constituted by a rigid body with a cavity that is completely filled with a Navier-Stokes liquid, and that moves in absence of external forces (inertial motions). Our investigation shows, in particular, that the ultimate motion of S about its center of mass is a permanent rotation, thus proving a longstanding conjecture of N.Ye. Zhukovskii. We also present other interesting features of inertial motions that are emphasized by our numerical tests, but that still lack a rigorous mathematical proof. © 2013 Académie des sciences

show abstract

mentioning

confidence: 88%

Inertial motions of a rigid body with a cavity filled with a viscous liquid

Galdi

Mazzone

Zunino

2013

Comptes Rendus. Mécanique

View full text Add to dashboard Cite

show abstract

“…Besides the interest for the applications, there have been numerous mathematical contributions which can be tracked back to the work by Stokes [32], Zhukovskii [34], Hough [8], Poincaré [18], and Sobolev [31], mostly concerned with ideal fluids. In recent years, new stability results have been derived: they are obtained for suitable geometrical configurations of S and/or by linearizing the equations of motion ( [23,24,25,2,30,13,12,16,11]). In [29,14], the class of weak solutions à la Leray-Hopf, corresponding to initial data having finite total kinetic energy, has been proved to be nonempty.…”

Section: Introduction and Formulation Of The Problemmentioning

confidence: 99%

A Maximal Regularity Approach to the Study of Motion of a Rigid Body with a Fluid-Filled Cavity

Mazzone

Prüß

Simonett

2019

J. Math. Fluid Mech.

View full text Add to dashboard Cite

We consider the inertial motion of a rigid body with an interior cavity that is completely filled with a viscous incompressible fluid. The equilibria of the system are characterized and their stability properties are analyzed. It is shown that equilibria associated with the largest moment of inertia are normally stable, while all other equilibria are normally hyperbolic.We show that every Leray-Hopf weak solution converges to an equilibrium at an exponential rate. In addition, we determine the critical spaces for the governing evolution equation, and we demonstrate how parabolic regularization in time-weighted spaces affords great flexibility in establishing regularity of solutions and their convergence to equilibria.2010 Mathematics Subject Classification. Primary: 35Q35, 35Q30, 35B40, 35K58, 76D05.

show abstract

“…In contrast, there is a large literature dealing with the motion of fluid-filled rigid bodies with no-slip boundary conditions, it spans from the early work by Stokes [38], Zhukovskii [42], Hough [11], Poincaré [26], and Sobolev [35] to more recent contributions mostly concerned with stability problems ( [32,33,21,4,15,13,12,34,16,9,5,17]). A comprehensive study of the motion of fluid-filled rigid bodies has recently been given in [8] (in an L 2 framework), and in [18] (in a more general L q framework).…”

Section: Introduction and Formulation Of The Problemmentioning

confidence: 99%

On the Motion of a Fluid-Filled Rigid Body with Navier Boundary Conditions

Mazzone¹,

Prüß²,

Simonett³

2019

SIAM J. Math. Anal.

View full text Add to dashboard Cite

We consider the inertial motion of a system constituted by a rigid body with an interior cavity entirely filled with a viscous incompressible fluid. Navier boundary conditions are imposed on the cavity surface. We prove the existence of weak solutions and determine the critical spaces for the governing evolution equation. Using parabolic regularization in time-weighted spaces, we establish regularity of solutions and their long-time behavior. We show that every weak solution à la Leray-Hopf to the equations of motion converges to an equilibrium at an exponential rate in the Lq-topology for every fluid-solid configuration.A nonlinear stability analysis shows that equilibria associated with the largest moment of inertia are asymptotically (exponentially) stable, whereas all other equilibria are normally hyperbolic and unstable in an appropriate topology.

show abstract

On the stability of a top with a cavity filled with a viscous fluid

Cited by 16 publications

References 11 publications

Inertial motions of a rigid body with a cavity filled with a viscous liquid

Inertial motions of a rigid body with a cavity filled with a viscous liquid

A Maximal Regularity Approach to the Study of Motion of a Rigid Body with a Fluid-Filled Cavity

On the Motion of a Fluid-Filled Rigid Body with Navier Boundary Conditions

Contact Info

Product

Resources

About