The existence and the regularity of the particle trajectory flow X(x, t) along a velocity field u on $mathbb{R}^n$ are discussed under the BMO-blow-up condition: $${int}_{0}^{T}{parallel}{omega}({ au}){parallel}_{BMO}d{ au}<{infty}$$ of the vorticity ${omega}{equiv}{ abla}{ imes}u$. A comment on our result related with the mystery of turbulence is presented.