Is the three dimensions Navier-Stokes equations problem a P problem?

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Edited. If we define this problem by a yes/no question, like:

« Does the 3D Navier-Stokes equations problem have a positive solution (which means that there are respecting problem conditions solutions for any respecting problem conditions initial velocity)? »…

…is this problem in P?

The P vs NP problem where is findable a formal definition of P

The 3D Navier-Stokes problem

->It seems not because we would have to test an infinite number of different initial velocities (respecting problem conditions) simultaneously in one algorithm?

But couldn’t it be simplified/reduced? Like can’t a Turing machine nevertheless do the job « ignoring » the ignorance of the initial velocity?

This subject mixes computer science and pure mathematics.

I’ve been looking at this subject: How to prove that problem is not in P?

But, being really noob in computer science, I don’t know how to begin to prove that the problem is not or is in P yet.

Any help is much appreciated.