MHD interaction of pulsar wind nebulae with SNRs and with the ISM

In the late 1960s the discovery of the Crab pulsar in its associated supernova remnant, launched a new field in supernova remnant research: the study of pulsar-driven or plerionic supernova remnants. In these type of remnants, the relativistic wind emitted by the pulsar, blows a pulsar wind nebula into the interior of its supernova remnant. Now, more then forty years after the discovery of the Crab pulsar, there are more then fifty plerionic supernova remnants known, due to the ever-increasing capacity of observational facilities. These observational studies reveal a Zoo of complex morphologies over a wide range of frequencies, indicating the significance of the interaction between a pulsar wind nebula with its surrounding supernova remnant. A pulsar which gained a kick velocity at birth, will ultimately break outside of its remnant, after which the pulsar wind nebula interacts directly with the interstellar medium. In general these pulsar wind nebulae are bounded by a bow shock, due to the supersonic motion of the pulsar. There are a few examples known of these pulsar-powered bow shocks, a number which is slowly increasing.I will review our current understanding of the different evolutionary stages of a pulsar wind nebula as it is interacting with its associated supernova remnant. Therefore, I will discuss both analytical and more recent numerical (M)HD models. The four main stages of a pulsar wind nebula are: the supersonic expansion stage, the reverse shock interaction stage, the subsonic expansion stage and ultimately the stage when the head of the bubble is bounded by a bow shock, due to the supersonic motion of the pulsar. Ultimately this pulsar wind nebula bow shock will break through its associated remnant, after which the pulsar-powered bow shock will interact directly with the interstellar medium. I will discuss recent numerical models from these type of pulsar wind nebulae and their morphology.