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REMARK ON PARTICLE TRAJECTORY FLOWS WITH UNBOUNDED VORTICITY

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The existence and the regularity of the particle trajectory ow X(x; t) along a velocity eld u on Rn are discussed under the BMO-blow-up condition:Z T0k!( )kBMOd < 1of the vorticity !  r  u. A comment on our result related with the mystery of turbulence is presented.

1. Background and the main assertion

2. The argument

3. Remarks connected with turbulence

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