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arXiv · 2402.07780

On the Asymptotic Behavior in Time of the Kinetic Energy in a Rigid Body-Liquid Problem

Giovanni P. Galdi·Paolo Maremonti
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Abstract

We give sufficient conditions on the initial data for the decay in time of the kinetic energy, $E$, of solutions to the system of equations describing the motion of a rigid body in a Navier-Stokes liquid. More precisely, assuming the initial data ``small" in appropriate norm, we show that if, in addition, the initial velocity field of the liquid, $v_0$, is in $L^q$, $q\in(1,2)$, then $E(t)$ vanishes as $t\to\infty$ with a specific order of decay. The order remains, however, unspecified if $v_0\in L^2$.

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Giovanni P. Galdi, Paolo Maremonti. 2024-02-12. On the Asymptotic Behavior in Time of the Kinetic Energy in a Rigid Body-Liquid Problem. https://arxiv.org/abs/2402.07780

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