Tangential Boundary Stabilization of Navier Stokes Equations is popular PDF and ePub book, written by Viorel Barbu in 2006, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Tangential Boundary Stabilization of Navier Stokes Equations can be Read Online from any device for your convenience.
Tangential Boundary Stabilization of Navier Stokes Equations Book PDF Summary
In order to inject dissipation as to force local exponential stabilization of the steady-state solutions, an Optimal Control Problem (OCP) with a quadratic cost functional over an infinite time-horizon is introduced for the linearized N-S equations. As a result, the same Riccati-based, optimal boundary feedback controller which is obtained in the linearized OCP is then selected and implemented also on the full N-S system. For $d=3$, the OCP falls definitely outside the boundaries of established optimal control theory for parabolic systems with boundary controls, in that the combined index of unboundedness--between the unboundedness of the boundary control operator and the unboundedness of the penalization or observation operator--is strictly larger than $\tfrac{3}{2}$, as expressed in terms of fractional powers of the free-dynamics operator. In contrast, established (and rich) optimal control theory [L-T.2] of boundary control parabolic problems and corresponding algebraic Riccati theory requires a combined index of unboundedness strictly less than 1. An additional preliminary serious difficulty to overcome lies at the outset of the program, in establishing that the present highly non-standard OCP--with the aforementioned high level of unboundedness in control and observation operators and subject, moreover, to the additional constraint that the controllers be pointwise tangential--be non-empty; that is, it satisfies the so-called Finite Cost Condition [L-T.2].
Detail Book of Tangential Boundary Stabilization of Navier Stokes Equations PDF
- Author : Viorel Barbu
- Release : 01 October 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821838747
- Genre : Mathematics
- Total Page : 146 pages
- Language : English
- PDF File Size : 12,9 Mb
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