I have a flow defined on a Whitney stratified set that is Lipschitz away from the singular set, and behaves well with respect to time (i.e., vectors violating Lipschitz condition have length going to zero before the vectors exhibiting Lipschitz behavior across the singular set reach the singular set). I would like to construct a global solution that is Lipschitz on each stratum and not too horrible on the singular set. It seems like the usual Euler scheme approach might be possible with some careful handling of the singular set.
Is there any work on this? Pointers to references would be much appreciated. Or are my google searches not returning anything useful because this approach is doomed?