Stabilizability of 2D and 3D Navier-Stokes equations with memory around a non-constant steady state Article Swipe
Wasim Akram
,
Manika Bag
,
Manil T. Mohan
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2502.00517
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2502.00517
In this article, we investigate the stabilizability of the two- and three-dimensional Navier-Stokes equations with memory effects around a non-constant steady state using a localized interior control. The system is first linearized around a non-constant steady state and then reformulated into a coupled system by introducing a new variable to handle the integral term. Due to the presence of variable coefficients in the linear operator, the rigorous computation of eigenvalues and eigenfunctions becomes infeasible. Therefore, we concentrate on the principal operator, and investigate its analyticity and spectral properties. We establish a feedback stabilization result for the principal system, ensuring a specific decay rate. Using the feedback operator derived from this analysis, we extend the approach to the full system, constructing a closed-loop system. By proving a suitable regularity result and applying a fixed-point argument, we ultimately demonstrate the stabilizability of the full system. We also discuss the stabilizability of the corresponding vorticity equation around a non-constant steady state.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2502.00517
- https://arxiv.org/pdf/2502.00517
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4407123678
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W4407123678Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2502.00517Digital Object Identifier
- Title
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Stabilizability of 2D and 3D Navier-Stokes equations with memory around a non-constant steady stateWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2025Year of publication
- Publication date
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2025-02-01Full publication date if available
- Authors
-
Wasim Akram, Manika Bag, Manil T. MohanList of authors in order
- Landing page
-
https://arxiv.org/abs/2502.00517Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2502.00517Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2502.00517Direct OA link when available
- Concepts
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Constant (computer programming), Steady state (chemistry), State (computer science), Navier–Stokes equations, Mathematics, Mathematical analysis, Physics, Mechanics, Computer science, Algorithm, Compressibility, Chemistry, Physical chemistry, Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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