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Asymptotic Properties And Separation Rates For Navier-Stokes Flows, Patrick Michael Phelps
Asymptotic Properties And Separation Rates For Navier-Stokes Flows, Patrick Michael Phelps
Graduate Theses and Dissertations
In this dissertation, we investigate asymptotic properties of local energy solutions to the Navier-Stokes equations and develop an application which controls the separation of non-unique solutions in this class. Specifically, we quantify the rate at which two, possibly unique solutions evolving from the same data may separate pointwise away from a singularity. This is motivated by recent results on non-uniqueness for forced and unforced Navier-Stokes and analytical and numerical evidence suggesting non-uniqueness in the Leray class. Our investigation begins with discretely self-similar solutions known to exist globally in time and to be regular outside a space-time paraboloid. We prove decay …