EN
We investigate the transport equation $∂_{t}u(t,x) + b(t,x)·D_{x}u(t,x) = 0$. Our result improves the classical criteria of uniqueness of weak solutions in the case of irregular coefficients: b ∈ BV, $div_x b ∈ BMO$. To obtain our result we use a procedure similar to DiPerna and Lions's one developed for Sobolev vector fields. We apply renormalization theory for BV vector fields and logarithmic type inequalities to obtain energy estimates.