well-posedness of Fokker-Planck equation (especially uniqueness) with rough coefficients is a quite involved problem. Since $a$ and $b$ possess less regularities and $\sL^{a,b}_t$ is a degenerate operator, the direct analytical approach seems not work (cf. [@Bo-Kr-Ro1; @Bo-Kr-Ro2]). Let $\cP(\mR^{2d})$ be the set of all probability measures on $\mR^{2d}$. We shall use a probabilistic method to prove the following result. \[Main2\] Suppose that $\sigma$ satisfies [**(UE)**]{} and for any $T>0$, $$\lim_{|z-z'|\to 0}\sup_{t\in[0,T]}\|\sigma_t(z)-\sigma_t(z')\|=0,$$ and $b\in L^q_{loc}(\mR_+; L^q(\mR^{2d}))$ for some $q\in(2(2d+1),\infty]$. Then for any $\nu\in\cP(\mR^{2d})$, there exists a unique probability measure-valued solution $\mu_t\in\cP(\mR^{2d})$ to in the distributional sense in the class that $t\mapsto\mu_t$ is weakly continuous with $\mu_0=\nu$ and $$\int^t_0\!\!\int_{\mR^{2d}}(|\v|+|b_s(x,\v)|)\mu_s(\dif x,\dif\v)\dif s<\infty,\ \ t>0.$$

The proof of this result is based on Figalli and Trevisan’s superposition characterization for the solutions of Fokker-Planck equation in terms of martingale problem associated with $\sigma$ and $b$. More precisely, Figalli [@Fi] and Trevisan [@Tre] showed that for any weakly continuous probability measure-valued solution $\mu_t$ of with initial value $\nu\in\cP(\mR^{2d})$, there exists a martingale solution for operator $\sL^{a,b}_t$ (a probability measure $\mP_\nu$ over the space of all continuous functions from $\mR_+$ to $\mR^{2d}$ denoted by $\Omega$) such that for all $t\in\mR_+$, $$\int_{\mR^{2d}}\varphi(z)\mu_t(\dif z)=\int_{\Omega}\varphi(\omega_t)\mP_\nu(\dif \omega),$$ where $t\mapsto\omega_t$ is the 