Dynamics of Partial Differential Equations

✍ Scribed by C. Eugene Wayne, Michael I. Weinstein

Publisher: Springer International Publishing
Year: 2015
Tongue: English
Leaves: 90
Series: Frontiers in Applied Dynamical Systems: Reviews and Tutorials 3
Edition: 1st ed. 2015
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently.

Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties and results about radiation damping where waves lose energy through radiation.

The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equations with very different physical origins and mathematical properties.

✦ Table of Contents

Front Matter....Pages i-x
Dynamical Systems and the Two-Dimensional Navier-Stokes Equations....Pages 1-40
Localized States and Dynamics in the Nonlinear Schrödinger/Gross-Pitaevskii Equation....Pages 41-79

✦ Subjects

Partial Differential Equations; Dynamical Systems and Ergodic Theory

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