Approximation of time-periodic flow past a translating body by flows in bounded domains
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915420205744128 |
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| author | Eiter, Thomas Silvestre, Ana Leonor |
| author_facet | Eiter, Thomas Silvestre, Ana Leonor |
| contents | We consider a time-periodic incompressible three-dimensional Navier-Stokes flow past a translating rigid body. In the first part of the paper, we establish the existence and uniqueness of strong solutions in the exterior domain $Ω\subset {\mathbb R}^3$ that satisfy pointwise estimates for both the velocity and pressure. The fundamental solution of the time-periodic Oseen equations plays a central role in obtaining these estimates. The second part focuses on approximating this exterior flow within truncated domains $Ω\cap B_R$, incorporating appropriate artificial boundary conditions on $\partial B_R$. For these bounded domain problems, we prove the existence and uniqueness of weak solutions. Finally, we estimate the error in the velocity component as a function of the truncation radius $R$, showing that, as $R \to \infty$, the velocities of the truncated problems converge, in an appropriate norm, to the velocity of the exterior flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximation of time-periodic flow past a translating body by flows in bounded domains Eiter, Thomas Silvestre, Ana Leonor Analysis of PDEs 35Q30, 76D05, 76D07, 35B10 We consider a time-periodic incompressible three-dimensional Navier-Stokes flow past a translating rigid body. In the first part of the paper, we establish the existence and uniqueness of strong solutions in the exterior domain $Ω\subset {\mathbb R}^3$ that satisfy pointwise estimates for both the velocity and pressure. The fundamental solution of the time-periodic Oseen equations plays a central role in obtaining these estimates. The second part focuses on approximating this exterior flow within truncated domains $Ω\cap B_R$, incorporating appropriate artificial boundary conditions on $\partial B_R$. For these bounded domain problems, we prove the existence and uniqueness of weak solutions. Finally, we estimate the error in the velocity component as a function of the truncation radius $R$, showing that, as $R \to \infty$, the velocities of the truncated problems converge, in an appropriate norm, to the velocity of the exterior flow. |
| title | Approximation of time-periodic flow past a translating body by flows in bounded domains |
| topic | Analysis of PDEs 35Q30, 76D05, 76D07, 35B10 |
| url | https://arxiv.org/abs/2507.23697 |