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