The easiest way to deal with the problem is to ignore her. If you respond to her or do anything to show you are agitated then she might be encouraged to continue. If she gets no response out of you then she will likely stop.
If you think these untrue rumors have actually caused some kind of harm (other than your hurt feelings) you can talk to a local attorney about potential slander, but that is likely a battle not worth fighting.
Unless the postings have caused you damages (loss of job, income, physical harm etc) you hav eno legal recourse. What you really have here is a failure on either one or both of your parts to move forward after break up. This is a relationship issue not really a legal one.