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

被引：0
作者：
Giusy Mazzone
Jan Prüss
Gieri Simonett
机构：
[1] Queen’s University,Department of Mathematics and Statistics
[2] Martin-Luther-Universität Halle-Wittenberg,Institut für Mathematik
[3] Vanderbilt University,Department of Mathematics
来源：
Journal of Mathematical Fluid Mechanics | 2019年 / 21卷
关键词：
Normally stable; Normally hyperbolic; Global existence; Critical spaces; Fluid–solid interactions; Rigid body motion; Primary 35Q35; 35Q30; 35B40; 35K58; 76D05;
D O I：
暂无
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摘要：
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.
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[11]  
Hough SS(2009)On the precession of deformable bodies J. Differ. Equ. 246 3902-3931
[12]  
Kostyuchenko AG(2017)Critical spaces for quasilinear parabolic evolution equations and applications J. Evol. Equ. 17 1381-1388
[13]  
Shkalikov AA(1960)On convergence of solutions to equilibria for quasilinear parabolic problems Prikl. Math. Mekh. 24 603-609
[14]  
Yurkin MY(1962)Addendum to the paper “On quasilinear parabolic evolution equations in weighted Prikl. Math. Mekh. 26 977-991
[15]  
Lyashenko AA(1963)-spaces II” Izvestiya AN SSSR, Mekhan. i mashinostr. 6 119-140
[16]  
Noll A(2012)About the stability of the motion of a top having a cavity filled with a viscous fluid Proc. R. Soc. Edinb. Sect. A 142 391-423
[17]  
Saal J(1974)On the stability of stationary motions of rigid bodies with cavities containing fluid PMM 38 980-985
[18]  
Poincaré H(1960)Lyapunov methods in the study of the stability of motion of solid bodies with liquid-filled cavities Zh. Prikl. Mekh. Tekhn. Fiz. 3 20-55
[19]  
Prüss J(undefined)On the motion of a rigid body with a cavity filled with a viscous liquid undefined undefined undefined-undefined
[20]  
Simonett G(undefined)Stabilization of free rotation of an asymmetric top with cavities completely filled with a liquid undefined undefined undefined-undefined
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