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;
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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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共 33 条
[1]  
Disser K(2016)Inertial motions of a rigid body with a cavity filled with a viscous liquid Arch. Ration. Mech. Anal. 221 487-526
[2]  
Galdi GP(1962)On the non-stationary Navier–Stokes system Rend. Sem. Mat. Univ. Padova 32 243-260
[3]  
Mazzone G(2013)Inertial motions of a rigid body with a cavity filled with a viscous liquid C. R. Méc. 341 760-765
[4]  
Zunino P(1985)Domains of fractional powers of the Stokes operator in Arch. Ration. Mech. Anal. 89 251-265
[5]  
Fujita H(1895) spaces Philos. Trans. R. Soc. Lond. 186 469-506
[6]  
Kato T(1998)The oscillations of a rotating ellipsoidal shell containing fluid Funct. Anal. Appl. 32 100-113
[7]  
Galdi GP(1993)On the stability of a top with a cavity filled with a viscous fluid Jpn. J. Ind. Appl. Math. 10 451-459
[8]  
Mazzone G(2003)On the instability of a rotating body with a cavity filled with viscous liquid Math. Z. 244 651-688
[9]  
Zunino P(1910)-calculus for the Stokes operator on Bull. Astron. 27 321-356
[10]  
Giga Y(2018)-spaces J. Differ. Equ. 264 2028-2074
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