\\ & = - { \lim _{\delta \searrow 0}}{ \int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\! \left ( 0 - { \chi \left ( \frac{|v|}{\delta}\right)}\right ) \frac{r}{|v|} { \left ( I - \frac{v \otimes v}{|v|^0} \right ) }a \cdot (\nabla _v \