Control at a distance of the motion of a rigid body immersed in a two-dimensional viscous incompressible fluid
| Autor: | József J. Kolumbán |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
010102 general mathematics Mathematical analysis Perturbation (astronomy) Rigid body 01 natural sciences Physics::Fluid Dynamics 010101 applied mathematics Controllability Boundary layer symbols.namesake Amplitude Euler's formula symbols 0101 mathematics Asymptotic expansion Navier–Stokes equations Analysis Mathematics |
| Zdroj: | Journal of Differential Equations. 269:764-831 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2019.12.021 |
| Popis: | We consider the motion of a rigid body immersed in a two-dimensional viscous incompressible fluid with Navier slip-with-friction conditions at the solid boundary. The fluid-solid system occupies the whole plane. We prove the small-time global exact controllability of the position and velocity of the solid when the control takes the form of a distributed force supported in a compact subset (with nonvoid interior) of the fluid domain, away from the body. The strategy relies on the introduction of a small parameter: we consider fast and strong amplitude controls for which the “Navier-Stokes+rigid body” system behaves like a perturbation of the “Euler+rigid body” system. By the means of a multi-scale asymptotic expansion we construct a controlled solution to the “Navier-Stokes+rigid body” system thanks to some controlled solutions to “Euler+rigid body”-type systems and by using that the influence of the boundary layer on the solid motion turns out to be sufficiently small. |
| Databáze: | OpenAIRE |
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