Year: 2026
Type: preprint
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 $L^2$ 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.
Source: arXiv (Cornell University)
Author: Cissé, Amadou
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208777555