Abstract
Pulsar wind nebulae inside young supernova remnants, and in particular the Crab nebula, are probably the best laboratories for high-energy astrophysics and relativistic plasma physics. They have been modeled numerically for more than a decade through multi-dimensional relativistic MHD simulations, relying on axial symmetry until a few years ago while currently using full three-dimensional simulations employing adaptive meshes. Here, we discuss the most recent findings, especially those obtained by our Arcetri group, focusing on the problem of magnetic field dissipation inside the nebula.
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