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Dynamics of Partial Differential Equations

  • C. Eugene Wayne
  • Michael I. Weinstein

Part of the Frontiers in Applied Dynamical Systems: Reviews and Tutorials book series (FIADS, volume 3)

Table of contents

About this book

Introduction

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.

Keywords

Navier-Stokes equation dispersive partial differential equations dissipative partial differentil equations dynamical systems nonlinear Shroedinger equation

Authors and affiliations

  • C. Eugene Wayne
    • 1
  • Michael I. Weinstein
    • 2
  1. 1.Department of Mathematics and StatisticsBoston UniversityBostonUSA
  2. 2.Dept. of Applied Physics & AppliedColumbia UniversityNew YorkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-19935-1
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-19934-4
  • Online ISBN 978-3-319-19935-1
  • Series Print ISSN 2364-4532
  • Series Online ISSN 2364-4931
  • Buy this book on publisher's site
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