Note on the problem of motion of viscous fluid around a rotating and translating rigid body

0540651 - MÚ 2022 RIV CZ eng J - Článek v odborném periodiku
Deuring, P. - Kračmar, Stanislav - Nečasová, Šárka
Note on the problem of motion of viscous fluid around a rotating and translating rigid body.
Acta Polytechnica. Roč. 61, SI (2021), s. 5-13. ISSN 1210-2709. E-ISSN 1805-2363
Grant CEP: GA ČR(CZ) GA19-04243S
Institucionální podpora: RVO:67985840
Klíčová slova: artificial boundary conditions * estimates of pressure * exterior domain * incompressible fluid
Obor OECD: Pure mathematics
Způsob publikování: Open access
https://doi.org/10.14311/AP.2021.61.0005

We consider the linearized and nonlinear systems describing the motion of incompressible flow around a rotating and translating rigid body D in the exterior domain Ω = R3 D, where D ⊂ R3 is open and bounded, with Lipschitz boundary. We derive the L∞-estimates for the pressure and investigate the leading term for the velocity and its gradient. Moreover, we show that the velocity essentially behaves near the infinity as a constant times the first column of the fundamental solution of the Oseen system. Finally, we consider the Oseen problem in a bounded domain ΩR:= BR ∩ Ω under certain artificial boundary conditions on the truncating boundary ∂BR, and then we compare this solution with the solution in the exterior domain Ω to get the truncation error estimate.
Trvalý link: http://hdl.handle.net/11104/0318272