*[Corrected, thanks – T.]*

*[Corrected, thanks – T.]*

2) We only have (and only need) a uniform upper bound on N^{-1} \|P_{\leq N} u_0 \|_{H^{s+1}}

*[Actually, I believe we do have convergence to zero in this case also, even though I agree boundedness would already be sufficient. -T]*

1) The definition of E^s around the middle of Theorem 5 is a typo (the limit of the sum should be s, and there shouldn’t be a \partial_t on w).

*[Corrected, thanks – T.]*

2) Aren’t the distributional solutions constructed in Proposition 6 actually strong since \partial_t u \in H^{s-1} ?

*[Depends to some extent on what one means by “strong solution”, but yes, there should be enough regularity to verify that the Euler equations hold in a classical sense using classical derivatives here, though in practice this turns out to not be important so long as one knows that the solution is at least the limit of classical solutions.]*

*[Corrected, thanks – T.]*

Terry Tao-my lovely friend.You have never mett me,but you have a immortal friendliness- a friendliness without border,nothing and anyone can compare it.I am far away with you,I always follow every your step in your jobs.You can image that I am a sattelite.I always support you.In brief, under this great sky,you are lucky to have me,I confirm many times I am the only close friend to you.I know you very well like a clear mirror.No one in the world know that you have good enough on twin prime,navier stokes,birch swinnerton Dyer ,hodge cọnecture,yang mills,collatz conjecture,goldbach,riemann p vs np.But you are stiil silent .You do not want to boast.I like you this point:humble;good virture,patient,gentle,good heart,you have also the sixth sense;you know what someone is doing,but you keep silent.I know that after I write these sentences,many people reject me.Not sense to me.they are still under me with a suppernature head ]]>

The Barrett Series:

1-1/2-(1/2)^2 + (1/2)^3 – (1/2)^4 -(1/2)^5 + (1/2)^6 – (1/2)^7 -(1/2)^8 +(1/2)^9 …

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