EAN: 9783319199344

DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS - C ...

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.

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