A new proof of the uniqueness of the flow for ordinary differential equations with \(BV\) vector fields (Q628611)

The authors give sufficient conditions for the existence and uniqueness of almost-flow solutions of the following initial value problem: \[ \begin{cases} X'(t)= b(t,X(t,x)) &\text{for all } t\in\mathbb R,\\ X(0,x)= x, \end{cases} \] where \(\Omega\) is a space of initial conditions and \(b\) is a BV vector field in \(L^{\infty}\) or \(L^1\). The results are based on a technique introduced in [C. R., Math., Acad. Sci. Paris 344, No.~12, 759--764 (2007; Zbl 1132.34043)].