The magnetorotational and Tayler instabilities in the pulsar magnetosphere

The magnetospheres around neutron stars should be very particular because of their strong magnetic field and rapid rotation. A study of the pulsar magnetospheres is of a crucial importance since it is the key issue to understand how energy inflow to the exterior is produced. In this paper, I discuss magnetohydrodynamic processes in the pulsar magnetosphere. I consider in detail the properties of magnetohydrodynamic waves that can exist in the magnetosphere and their instabilities.These instabilities lead to formation of magnetic structures and can be responsible for a short-term variability ofthe pulsar emission.