Spatial and temporal damping of fluid perturbation at a distance Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/7d278v35w

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  • A recent article by Cozzi and Kelliher [3] has demonstrated a sense of "locality" to the incompressible Euler equations which mirrors physical fluid behavior. We further develop the corresponding notion of "damping," and identify both temporal and local damping behaviors. To represent this problem, we perturb the initial condition of a fluid system in R^d and bound the effects of this perturbation at later times. We extend the previous L^2 result to the incompressible Navier-Stokes equations with any viscosity. Based on this result in $L^2$, we derive a similar bound in L^infinity. We discuss the analogies between these bounds and the contributions due to the perturbation to the total kinetic energy and maximum velocity within a compact region of interest.
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