Let $U \subset \mathbb{R}^n$ be open, let $I \subset \mathbb{R}$ be an interval, let $b \in C^1(U;\mathbb{R}^n)$, let $f \in C^0(U)$, and let $u \in C^1(U)$ satisfy the pointwise transport equation
for every $x \in U$. Let $\gamma \in C^1(I;U)$ be a classical solution of the [ordinary differential equation](/page/Ordinary%20Differential%20Equation)