Instability in Models Connected with Fluid Flows I [Paperback]

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.

Preface, Claude Bardos and Andrei Fursikov.- Solid Controllability in Fluid Dynamics, Andrey Agrachev and Andrey Sarychev.- Analyticity of Periodic Solutions of the 2D Boussinesq System, Maxim Arnold.- Nonlinear Dynamics of a System of Particle-Like Wavepackets, Anatoli Babin and Aleksander Figotin.- Attractors for Nonautonomous NavierStokes System and Other Partial Differential Equations, Vladimir Chepyzhov and Mark Vishik.- Recent Results in Large Amplitude Monophase Nonlinear Geometric Optics, Christophe Cheverry.- Existence Theorems for the 3DNavierStokes System Having as Initial Conditions Sums of Plane Waves, Efim Dinaburg and Yakov Sinai.- Bursting Dynamics of the 3D Euler Equations in Cylindrical Domains, Francois Golse, Alex Mahalov, and Basil Nicolaenko.- Increased Stability in the Cauchy Problem for Some Elliptic Equations, Victor Isakov

Instability in Models Connected with Fluid Flows I presents chapters from world renowned specialists. The stability of mathematical models simulating physical processes is discussed in topics on control theory, first order linear and nonlinear equations, water waves, free boundary problems, large time asymptotics of solutions, stochastic equations, Euler equations, Navier-Stokes equations, and other PDEs of fluid mechanics.

Fields covered include: controllability and accessibility properties of the Navier- Stokes and Euler systems, nonlinear dynamics of particle-like wavepackets, attractors of nonautonomous Navier-Stokes l3Ä