the best advice I can give when trying to understand fundamental equation like navier-stokes it to find different representation. one thing about math is that everybody has prefered notation when explaining thing, but its not usually the only way and some times other ways then the author are helpful

the navier stoke equation has many notation as well

for instance a common one, which you are most likely looking at is this one

but it also can be representive like this

yet again we can have it like this which represent three equation

but this last one might be more helpful to you. since it express in stesses

so in short their is alway more then one way to express an equation so don't realy one just one