  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.
