Suppose I am given a system that consists of a distribution of charged particles(which are all over space and are point-charges). They are described by a set of functions instead of variables. These functions are:
- $C(x)$ - a function describing the amount of charge at each point in space. For example, take the one dimensional example of $C(x) = \sin(x)$.
- $M(x)$ - a function describing the amount of mass at each point in space.
- $V(x)$ - the function describing what the sum of all the velocities of the particles at a point is.
Given these are the functions to describe the system at time $t = 0$, is it possible to predict the state of this system (the charge distribution, velocities and mass distributions) at a later time, say, $t = 2$, using Newtonian dynamics?
My system can be thought of as a fluid, where distribution of mass and charge vary. I ignore charges if that simplifies things. I want to take into account gravity, though, at least. How do I exactly proceed to find the distribution functions at $t = 2$?
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