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Utterly authoritative, with papers from world-renowned leaders in the field
Includes the very latest theories and results
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 systems, large amplitude monophase nonlinear geometric optics, existence results for 3D Navier-Stokes equations and smoothness results for 2D Boussinesq equations, instability of incompressible Euler equations, increased stability in the Cauchy problem for elliptic equations.
Contributors include: Andrey Agrachev (Italy-Russia) and Andrey Sarychev (Italy); Maxim Arnold (Russia); Anatoli Babin (USA) and Alexander Figotin (USA); Vladimir Chepyzhov (Russia) and Mark Vishik (Russia); Christophe Cheverry (France); Efim Dinaburg (Russia) and Yakov Sinai (USA-Russia); Francois Golse (France), Alex Mahalov (USA), and Basil Nicolaenko (USA); Victor Isakov (USA)
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 Navier–Stokes 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 3D–Navier–Stokes 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