[golwengaud]

It looks like the author is attacking statement C from the official problem description (http://www.claymath.org/millennium/Navier-Stokes_Equations/n...). That statement asks for "a smooth, divergence-free vector field u0 (x) on R3 and a smooth f(x, t) on R3 x [0, ∞), satisfying [some physical-reasonableness conditions] for which there exist no solutions (p, u) of the [the Navier-Stokes equation, a physical reasonableness condition, and a sort of sanity condition]." In essence, you're finding a counterexample for uniqueness.

The author claims to have found exactly such a combination of initial-value field u0(x) and force function f(x), solving the millenium problem. I can't really judge his claim yet, as I haven't read the whole paper (and I'm probably not qualified to say even once I have), but slackenemy presents some good reasons to be rather dubious elsewhere in the thread. Also, applying Scott Aaronson's "Eight Signs A Claimed P≠NP Proof Is Wrong" (http://scottaaronson.com/blog/?p=458) isn't pretty.