What does "dynamics" of PDEs mean? I have heard and seen many times in informal discussions the term "dynamics" of certain PDE. For instance, "the long time _dynamics_ of the 2D NSE is entirely contained in the global attractor". And even in the title of a journal: ![enter image description here]( What does "dynamics" mean in such a context? Does it have a formal definition in any references?

As a PhD candidate in Dynamical Systems, I would interpret this as a discussion about the more qualitative aspects of the PDE. Example topics (that would fall under a discussion of the dynamical system generated by a PDE acting on the space of possible initial conditions) might include

* Are there any steady-state solutions? Periodic solutions?

* Do these steady-state/periodic solutions attract or repel nearby initial conditions?

* What is the asymptotic behavior of solutions as $t \to \pm \infty$?

* Is there any _sensitive dependence on initial conditions_? I.e., do initial conditions that are "close" drift apart or converge? How quickly does this happen--linearly/exponentially / ... ?