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Paul Goulart (pgoulartcontrol.ee.ethz.ch) Abstract: This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed optimization methods based on sumofsquares decomposition to construct a polynomial Lyapunov function. We then show how these methods can be extended to infinite dimensional NavierStokes systems using robust optimization techniques. Crucially, this extension requires only the solution of infinitedimensional linear eigenvalue problems and finitedimensional sumofsquares optimization problems. We further show that subject to minor technical constraints, a general polynomial Lyapunov function is always guaranteed to provide better results than the classical energy methods in determining a lowerbound on the maximum Reynolds number for which a flow is globally stable, if the flow does remain globally stable for Reynolds numbers at least slightly beyond the energy stability limit. Such polynomial functions can be searched for efficiently using the SOS technique we propose. Keywords: NavierStokes; Flow stability; Sumofsquares; Lyapunov methods Category 1: Applications  Science and Engineering (Basic Sciences Applications ) Category 2: Applications  Science and Engineering (Optimization of Systems modeled by PDEs ) Category 3: Robust Optimization Citation: Working Paper, Imperial College London, January 2011 Download: [PDF] Entry Submitted: 01/06/2011 Modify/Update this entry  
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