Lots of real world physics problems contain a huge number of variables and therefore have very complicated equations describing their associated dynamics. An example of this is non-linear partial differential equations, which are notoriously difficult to solve. As an example, take the Navier-Stokes equations. These are real physics equations which describe the motions of fluids and their physical characteristics.
Nobody has yet solved the problem concerning global existence and uniqueness of these equations, and in fact it is one of the millenium prize problems owing to its difficulty. Relating to your question, we effectively have an equation describing a physics phenomena for which the mathematical tools are not yet sufficient to prove is well defined and as such it is difficult to talk about how precise the extracted physics is regarding the solution of this equation.