This talk is about my journey into mathematical physics research. In this talk, we consider the non-relativistic limit of Israel-Stewart theory with bulk and shear viscosity, which defines a non-Newtonian barotropic fluid. The conditions for local well-posedness and symmetric hyperbolicity are determined in 3+1 dimensions. Restricting to the case of bulk, we determine the conditions for the nonexistence of smooth solutions, and prove that these results can be extended to the full bulk + shear viscosity case as well. I will also discuss what led me to work on this problem and the process of solving it.
