TY  - BOOK
AU  - Wayne,C.Eugene
AU  - Weinstein,Michael I.
ED  - SpringerLink (Online service)
TI  - Dynamics of Partial Differential Equations
T2  - Frontiers in Applied Dynamical Systems: Reviews and Tutorials,
SN  - 9783319199351
AV  - QA370-380 
U1  - 515.353 23
PY  - 2015///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - mathematics
KW  - Dynamics
KW  - Ergodic theory
KW  - Partial Differential Equations
KW  - Mathematics
KW  - Dynamical Systems and Ergodic Theory
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-319-19935-1
ER  -