Representation formulas and far-field behavior of time-periodic incompressible viscous flow around a translating rigid body
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914685124608000 |
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| author | Eiter, Thomas Silvestre, Ana Leonor |
| author_facet | Eiter, Thomas Silvestre, Ana Leonor |
| contents | This paper is concerned with integral representations and asymptotic expansions of solutions to the time-periodic incompressible Navier-Stokes equations for fluid flow in the exterior of a rigid body that moves with constant velocity. Using the time-periodic Oseen fundamental solution, we derive representation formulas for solutions with suitable regularity. From these formulas, the decomposition of the velocity component of the fundamental solution into steady-state and purely periodic parts and their detailed decay rate in space, we deduce complete information on the asymptotic structure of the velocity and pressure fields. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_12213 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Representation formulas and far-field behavior of time-periodic incompressible viscous flow around a translating rigid body Eiter, Thomas Silvestre, Ana Leonor Analysis of PDEs 35Q30, 76D05, 76D07, 35B10, 35A08, 35C15, 35C20 This paper is concerned with integral representations and asymptotic expansions of solutions to the time-periodic incompressible Navier-Stokes equations for fluid flow in the exterior of a rigid body that moves with constant velocity. Using the time-periodic Oseen fundamental solution, we derive representation formulas for solutions with suitable regularity. From these formulas, the decomposition of the velocity component of the fundamental solution into steady-state and purely periodic parts and their detailed decay rate in space, we deduce complete information on the asymptotic structure of the velocity and pressure fields. |
| title | Representation formulas and far-field behavior of time-periodic incompressible viscous flow around a translating rigid body |
| topic | Analysis of PDEs 35Q30, 76D05, 76D07, 35B10, 35A08, 35C15, 35C20 |
| url | https://arxiv.org/abs/2402.12213 |