03308nam a22004935i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118041000800153050001400161072001700175072002300192082001400215100002800229245008600257260005900343264005900402300003400461336002600495337002600521338003600547347002400583490005500607505025300662520144900915650001702364650003702381650002002418650002702438650001702465650001302482650002902495650002902524650003602553650003202589710003402621773002002655776003602675830005502711856004802766978-0-85729-043-4DE-He21320141014113434.0cr nn 008mamaa101119s2011 xxk| s |||| 0|eng d a97808572904347 a10.1007/978-0-85729-043-42doi aeng 4aTJ212-225 7aTJFM2bicssc 7aTEC0040002bisacsh04a629.82231 aBarbu, Viorel.eauthor.10aStabilization of Navier–Stokes Flowsh[electronic resource] /cby Viorel Barbu. 1aLondon :bSpringer London :bImprint: Springer,c2011. 1aLondon :bSpringer London :bImprint: Springer,c2011. aXII, 276 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aCommunications and Control Engineering,x0178-53540 aPreliminaries -- Stabilization of Abstract Parabolic Systems -- Stabilization of Navier–Stokes Flows -- Stabilization by Noise of Navier–Stokes Equations -- Robust Stabilization of the Navier–Stokes Equation via the H-infinity Control Theory. aStabilization of Navier–Stokes Flows presents recent notable progress in the mathematical theory of stabilization of Newtonian fluid flows. Finite-dimensional feedback controllers are used to stabilize exponentially the equilibrium solutions of Navier–Stokes equations, reducing or eliminating turbulence. Stochastic stabilization and robustness of stabilizable feedback are also discussed. The text treats the questions: • What is the structure of the stabilizing feedback controller? • How can it be designed using a minimal set of eigenfunctions of the Stokes–Oseen operator? The analysis developed here provides a rigorous pattern for the design of efficient stabilizable feedback controllers to meet the needs of practical problems and the conceptual controllers actually detailed will render the reader’s task of application easier still. Stabilization of Navier–Stokes Flows avoids the tedious and technical details often present in mathematical treatments of control and Navier–Stokes equations and will appeal to a sizeable audience of researchers and graduate students interested in the mathematics of flow and turbulence control and in Navier-Stokes equations in particular. The chief points of linear functional analysis, linear algebra, probability theory and general variational theory of elliptic, parabolic and Navier–Stokes equations are reviewed in an introductory chapter and at the end of chapters 3 and 4. 0aEngineering. 0aDifferential equations, partial. 0aSystems theory. 0aHydraulic engineering.14aEngineering.24aControl.24aSystems Theory, Control.24aFluid- and Aerodynamics.24aPartial Differential Equations.24aEngineering Fluid Dynamics.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780857290427 0aCommunications and Control Engineering,x0178-535440uhttp://dx.doi.org/10.1007/978-0-85729-043-4