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arXiv · 2602.10678

Stabilization of nonautonomous Navier-Stokes flows under dynamic slip boundary conditions

Buddhika Priyasad·Sérgio S. Rodrigues
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Abstract

Exponential stabilizability of the incompressible Navier-Stokes equations under dynamic slip boundary conditions toward arbitrary time-dependent trajectories is proven. The feedback control law is constructed explicitly using oblique projections and realized through a finite number of spatially localized interior actuators, without requiring spectral assumptions. The approach extends to various slip boundary condition types (Navier, vorticity-type, and Neumann) and applies to multi-connected domains. Weak solution existence and exponential decay estimates are established, with the stabilization rate depending on the boundary dynamics parameters.

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Buddhika Priyasad, Sérgio S. Rodrigues. 2026-02-11. Stabilization of nonautonomous Navier-Stokes flows under dynamic slip boundary conditions. https://arxiv.org/abs/2602.10678

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