ABSTRACT

\nVerifying nonlinear stabil ity of a laminar fluid flow against all perturbations is a central challen ge in fluid dynamics. Past results rely on monotonic decrease of a perturb ation energy or a similar quadratic generalized energy. Existing methods a re unable to verify global stability for the many flows that seem to be st able despite these energies growing transiently. I will present a broadly applicable method to verify global stability of such flows. This method us es polynomial optimization computations to construct non-quadratic Lyapuno v functions that decrease monotonically. I will present an application of the method to 2D Couette flow\, where it verifies global stability at Reyn olds numbers above the energy stability threshold found by Orr in 1907. Th is is joint work with Federico Fuentes and Sergei Chernyshenko.

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BIO

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DTSTAMP:20200925T001124Z
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END:VCALENDARDavid Goluskin is an Assistant Professor of Ma thematics at the University of Victoria in British Columbia\, Canada. From 2014 to 2017 he was a James Van Loo Postdoctoral Fellow in the Mathematic s Department at the University of Michigan. He holds a PhD in Applied Math ematics from Columbia University. Dr. Goluskin’s research centers on flu id dynamics and related nonlinear dynamical PDEs and ODEs. Much of his wor k on fluids has focused on thermal convection\, incorporating direct numer ical simulation as well as theoretical analysis of topics including nonlin ear stability and a priori estimates of average quantities. His recent foc us has been the development of broadly applicable mathematical methods bas ed on computational convex optimization\, especially polynomial optimizati on.

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