https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness
Terence Tao on record saying he thinks NO.
"Does a smooth Navier-Stokes solution always exist?"
We proceed by contradiction.
If it were false, there would be counterexamples. Some people are smart and would find them.
They have not.
Thus all theorems and conjectures are true.
- Gigacasting’s First Law of Millennium Prizes and Other Famous Theorems
(🤔)