Consider a system of many point particles each having a certain mass and electric charge and certain initial velocity. This system is completely governed by the laws of gravitation and electromagnetic field. If this system is left on its own without any external influence, any physical quantity like velocity of a particle or electric field at a point, of this system will vary smoothly with time and space. (keeping aside any singularities that could occur eventually). My question is whether any such system which is governed by such laws of physics (except ofcourse QM) would remain smooth until the occurrence of a singularity, in the absence of any external influence.
PS : please feel free to edit/suggest changes to the question in case if it could make it more meaningful.