{ \mathrm{div}_v}\{ { f ^\varepsilon}{ (\alpha - \beta |v|^0) v}\} = 0,\;\;(t,x,v) \in {{{\bf}R}}_+ \times {{{\bf}R}}^d \times {{{\bf}R}}^d$$ $$\label{Equ00} { a ^\varepsilon}= - \nabla _x U \star \int _{{{{\bf}R}}^d} { f ^\varepsilon}\;{ \mathrm{d}}v - H \star { f ^\varepsilon}