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Instability in Models Connected with Fluid Flows I

:	Claude Bardos, Andrei Fursikov
:	Claude Bardos, Andrei V. Fursikov
:	Instability in Models Connected with Fluid Flows I
:	Springer-Verlag
:	9780387752174
:	1
:	CHF 132.90
:

:	Maschinenbau, Fertigungstechnik
:	English

:	364
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

In this authoritative and comprehensive volume, Claude Bardos and Andrei Fursikov have drawn together an impressive array of international contributors to present important recent results and perspectives in this area. The main subjects that appear here relate largely to mathematical aspects of the theory but some novel schemes used in applied mathematics are also presented. Various topics from control theory, including Navier-Stokes equations, are covered.

	Main Topics	7
	Editors	9
	Preface	10
	1. Overview	10
	2. Classification of Contributions and Comments	12
	3. Methods and Tools	21
	References	21
	Authors	23
	Content of Volume I	28
	Content of Volume II	32
	Solid Controllability in Fluid Dynamics	33
	1. Introduction	33
	2. 2D Navier–Stokes / Euler Equations Controlled by Degenerate Forcing. Definitions and Problem Setting	36
	3. Geometric Control. Accessibility and Controllability via Lie Brackets	43
	4. Computation of Brackets in Finite and Infinite Dimensions. Controlling along Principal Axes	49
	5. Controllability and Accessibility of Galerkin Approximations of Navier–Stokes / Euler Equations on T2	51
	6. Steady State Controlled Directions. Abstract Controllability Result for Navier– Stokes Equations	54
	7. Navier–Stokes and Euler Equations on T2	55
	8. Controllability of 2D Navier–Stokes Equations on Rectangular Domain	58
	9. Controllability on Generic Riemannian Surface Diffeomorphic to Disc	59
	10. Navier–Stokes / Euler Equations on Sphere S2	62
	References	65
	Analyticity of Periodic Solutions of the 2D Boussinesq System	68
	References	83
	Nonlinear Dynamics of a System of Particle- Like Wavepackets	84
	1. Introduction	85
	2. Statement of Results	94
	3. Conditions and Definitions	110
	4. Integrated Evolution Equation	120
	5. Wavepacket Interaction System	127
	6. Reduction of Wavepacket Interaction System to an Averaged Interaction System	136
	7. Superposition Principle and Decoupling of the Wavepacket Interaction System	150
	References	162
	Attractors for Nonautonomous Navier– Stokes System and Other Partial Differential Equations	166
	Introduction	166
	1. Attractors of Autonomous Equations	169
	2. Attractors of Nonautonomous Equations	192
	3. Kolmogorov e-Entropy of Global Attractors	231
	4. Nonautonomous 2D Navier–Stokes System with Singularly Oscillating External Force	250
	5. Uniform Global Attractor of Ginzburg–Landau Equation with Singularly Oscillating Terms	271
	References	287
	Recent Results in Large Amplitude Monophase Nonlinear Geometric Optics	297
	1. Introduction	297
	2. Case of Incompressible Euler Equations	301
	3. Large Amplitude Waves	305
	References	317
	Existence Theorems for the 3D– Navier– Stokes System Having as Initial Conditions Sums of Plane Waves	319
	References	329
	Bursting Dynamics of the 3D Euler Equations in Cylindrical Domains	331
	1. Introduction	332
	2. Vorticity Waves and Resonances of Elementary Swirling Flows	337
	3. The Strictly Resonant Euler Systems: the SO( 3) Case	345
	4. Strictly Resonant Euler Systems: the Case of 3- Wave Resonances on Small-Scales	356
	Appendix	363
	References	365
	Increased Stability in the Cauchy Problem for Some Elliptic Equations	369
	1. Introduction	369
	2. Energy Type Estimates in Low Frequency Zone	374
	3. Some Carleman Estimates	386
	4. Proofs of Theorems 1.1 and 1.2	388
	References	392
	Index	393