Comment What an idiotic statement (Score 2) 97
This would imply, at least theoretically, that the laws of physics themselves would break down under certain conditions: that, for example, water could be made to spontaneously explode.
The NS equations are just a model of the physics of fluids. Particularly, they assume a continuum whereas actual fluids, having molecules and such, are not a continuum. For most engineering problems, you can assume the fluid is a continuum. At very small scales, such as at a singularity, such an assumption is not valid. So, having the NS equations break down says nothing at all about the "laws of physics" (basic conservation laws) or how physical fluids might really behave. It's a mildly interesting result that existence is not a feature of the NS equations, but this is fodder for mathematician, not physicists.