Global well-posedness of solutions for the equations modelling the motion of a rigid body in a bidimensional perfect fluid
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918406468403200 |
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| author | You, Xiaoguang |
| author_facet | You, Xiaoguang |
| contents | This paper considers a system modelling the evolution of a rigid body immersed in a bidimensional incompressible perfect fluid. In the special case of a disk-shaped rigid body, it was shown by C. Rosier and L. Rosier (2009) that the system admits a unique global solution when the initial fluid velocity $u_0$ belongs to $H^s$ ($s \ge 3$) and its vorticity $\operatorname{curl} u_0$ lies in $L^p$ with $1 \le p < 2$. By establishing a Beale-Kato-Majda type bound, we generalize the result by removing the constraint $\operatorname{curl} u_0 \in L^p$ and allowing the rigid body to be of arbitrary shape. Moreover, we obtain an explicit energy bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23087 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of solutions for the equations modelling the motion of a rigid body in a bidimensional perfect fluid You, Xiaoguang Analysis of PDEs This paper considers a system modelling the evolution of a rigid body immersed in a bidimensional incompressible perfect fluid. In the special case of a disk-shaped rigid body, it was shown by C. Rosier and L. Rosier (2009) that the system admits a unique global solution when the initial fluid velocity $u_0$ belongs to $H^s$ ($s \ge 3$) and its vorticity $\operatorname{curl} u_0$ lies in $L^p$ with $1 \le p < 2$. By establishing a Beale-Kato-Majda type bound, we generalize the result by removing the constraint $\operatorname{curl} u_0 \in L^p$ and allowing the rigid body to be of arbitrary shape. Moreover, we obtain an explicit energy bound. |
| title | Global well-posedness of solutions for the equations modelling the motion of a rigid body in a bidimensional perfect fluid |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.23087 |