myw / navier_stokes_translate Goto Github PK

I hear the author himself has admitted there is a flaw in the proof. Is it serious enough to warrant discontinuing this translation?

based on tex file:

This estimate is arrived at easily if the k-th equation of the system is multi-
plied by uk , and, nothing...

the "nothing" should be "noting"?

"This result also enables the use of perturbation theory, and improving the smoothness of a solution with increasing smoothness in the problem data."

This is ungrammatical as it stands. If it means "this result also enables the use of perturbation theory and (also) enables improving the smoothness...." then the comma should be deleted. Otherwise the second independent clause is missing a verb. It may mean something else, but I'm an amateur at math AND Russian.
Maybe it should be something like "This result enables both the use of perturbation theory and improving the smoothness of a solution with increasing smoothness in the problem data."

Line 117 should be:
&\divr u \equiv \sum_{k=1}^{3} \pderiv{u_k}{x_k}= 0,\qquad (t,x) \in \Omega.
instead of:
&\divr u \equiv \sum_{k=1}^{3} = 0,\qquad (t,x) \in \Omega.

(sorry, I'm not familiar with GitHub - so I just leave this comment here... )

(I don't know Russian, hence the following is based entirely on the current translation.)

Line 58: "such great mathematicians a" → "such great mathematicians as".

Line 153-154: the sentence "We will denote [...]" sounds weird as it is, but sadly I don't have a better suggestion.

Line 157: "instead the period boundary conditions" → "instead of the periodic boundary conditions"

Line 168: "With $L_2(\Omega)$, as usual, we denote" → "As usual, $L_2(\Omega)$ denotes"

Line 180: the definition of \nabla should not contain p: replace "{p}" by "{}" twice.

Lines 181, 194 and 234 are not consistent in notations: "\langle u, \nabla u \rangle" versus "\langle u, \nabla \rangle u" versus "(u, \nabla)u". The second and third forms are likely better. I assume that this is present in the Russian original?

Line 221: "is not less than three" → "is at least three" or "is three or more"