On the Asymptotic Behavior in Time of the Kinetic Energy in a Rigid Body-Liquid Problem
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916122507345920 |
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| author | Galdi, Giovanni P. Maremonti, Paolo |
| author_facet | Galdi, Giovanni P. Maremonti, Paolo |
| contents | 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 $v_0\in L^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07780 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Asymptotic Behavior in Time of the Kinetic Energy in a Rigid Body-Liquid Problem Galdi, Giovanni P. Maremonti, Paolo Analysis of PDEs Mathematical Physics 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 $v_0\in L^2$. |
| title | On the Asymptotic Behavior in Time of the Kinetic Energy in a Rigid Body-Liquid Problem |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2402.07780 |