Disclinations in nematics in the presence of flexoelectricity

The stability problems of wedge disclinations (with pure splay and bend distortions) in nematic liquid crystals (NLC) are considered in the presence of flexoelectricity. We write NLC director equations in the cylindrical coordinate system, taking into account flexoelectricity. These equations allow us to solve many interesting problems on the influence of flexoelectricity on the orientational structures of NLC. In particular, it is shown that the line of disclination with radial distribution of director can be stabilized in the presence of flexoelectricity even far from nematicsmectic phase transition point. For the disclination with azimuthal distribution of director for all physical sizes the line is not stable and escapes in the third dimension.