Mathematicians have developed different definitions for how "smooth" a function might be. A function (e.g. from or to $\mathbb{R}^n$ or $\mathbb{C}^n$) might be continuous, or once-differentiable, or twice-differentiable, or infinitely differentiable (smooth), or analytic. I am interested in the question of how smooth the evolution of the universe is.
More precisely, for any physical theory, we can look at those trajectories in the relevant phase space (or configuration space) of that theory which conform to the laws of physics. For example, in classical mechanics, we can look at those trajectories in phase space that conform to Newton's laws. My question is the following:
Can it be shown that every trajectory in phase space/configuration space that conforms to Newton's Laws (or Maxwell's Laws, or the Schrodinger equation) is continuous/differentiable/smooth/analytic?
I realize this is a fairly open-ended question (because it asks about different laws of physics), but any partial answer would be appreciated.
