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arXiv · 2309.07006

Stabilization of 2D Navier-Stokes equations by means of actuators with locally supported vorticity

Sérgio S. Rodrigues·Dagmawi A. Seifu
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Abstract

Exponential stabilization to time-dependent trajectories for the incompressible Navier-Stokes equations is achieved with explicit feedback controls. The fluid is contained in two-dimensional spatial domains and the control force is, at each time instant, a linear combination of a finite number of given actuators. Each actuator has its vorticity supported in a small subdomain. The velocity field is subject to Lions boundary conditions. Simulations are presented showing the stabilizing performance of the proposed feedback. The results also apply to a class of observer design problems.

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Sérgio S. Rodrigues, Dagmawi A. Seifu. 2023-09-13. Stabilization of 2D Navier-Stokes equations by means of actuators with locally supported vorticity. https://doi.org/10.1007/s10883-023-09677-7

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