The spin evolution of the pulsars with non-rigid core

We formulate a model of pulsar spin evolution (braking, inclination angle evolution and radiative precession) taking into account the non-rigidity of neutron star rotation. We discuss two simple limiting cases of this model and show that the evolution of the inclination angle substantially depends on the model of crust-core interaction. The non-rigidity of core rotation accelerates the inclination angle evolution and makes all pulsars evolve to the orthogonal state. The size of the effect depends on the amount of differentially rotating matter and mechanism of its interaction with the rest of the star. Since the rapid volution of the inclination angle apparently contradicts the observational data, our results may be used as an additional test for the theories of the cores of neutron stars.