Stabilization of nonautonomous Navier-Stokes flows under dynamic slip boundary conditions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914322011127808 |
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| author | Priyasad, Buddhika Rodrigues, Sérgio S. |
| author_facet | Priyasad, Buddhika Rodrigues, Sérgio S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10678 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stabilization of nonautonomous Navier-Stokes flows under dynamic slip boundary conditions Priyasad, Buddhika Rodrigues, Sérgio S. Analysis of PDEs Optimization and Control 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. |
| title | Stabilization of nonautonomous Navier-Stokes flows under dynamic slip boundary conditions |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2602.10678 |