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PreprintCC BY 4.0arXiv

Energy Decay Induced by Localized Coercivity in the 3D Navier--Stokes Equations

  • Amadou Cissé
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Abstract

Energy-based analysis of the three-dimensional incompressible Navier--Stokes equations with spatially localized dissipation is developed at the level of kinetic energy and Leray--Hopf weak solutions. A localized coercivity property linking viscosity and damping to global L2 control is introduced and related to observability and spectral inequalities for the associated Stokes operator. Under this condition, exponential energy decay is established without regularity or linearization assumptions, and time-dependent damping is treated within a nonautonomous framework. A finite-dimensional spectral quantity is proposed as a computable proxy for coercivity, yielding explicit decay estimates for reduced-order models.

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Cite

BibTeXRIS
BibTeX
@misc{cisse2026energy,
  title = {{Energy Decay Induced by Localized Coercivity in the 3D Navier--Stokes Equations}},
  author = {Amadou Cissé},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03164},
  eprint = {2609.03164},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03164},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Energy Decay Induced by Localized Coercivity in the 3D Navier--Stokes Equations
AU  - Amadou Cissé
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.03164
UR  - https://arxiv.org/abs/2609.03164
AB  - Energy-based analysis of the three-dimensional incompressible Navier--Stokes equations with spatially localized dissipation is developed at the level of kinetic energy and Leray--Hopf weak solutions. A localized coercivity property linking viscosity and damping to global L^2 control is introduced and related to observability and spectral inequalities for the associated Stokes operator. Under this condition, exponential energy decay is established without regularity or linearization assumptions, and time-dependent damping is treated within a nonautonomous framework. A finite-dimensional spectral quantity is proposed as a computable proxy for coercivity, yielding explicit decay estimates for reduced-order models.
ER  -