  Here we briefly discuss the Einstein-Aether gravity theory by modification of
Einstein-Hilbert action. We find the modified Friedmann equations and then from
the equations we find the effective density and pressure for Einstein-Aether
gravity sector. These can be treated as dark energy provided some restrictions
on the free function $F(K)$, where $K$ is proportional to $H^{2}$. Assuming two
types of the power law solutions of the scale factor, we have reconstructed the
unknown function $F(K)$ from HDE and NADE and their entropy-corrected versions
(ECHDE and ECNADE). We also obtain the EoS parameter for Einstein-Aether
gravity dark energy. For HDE and NADE, we have shown that the type I scale
factor generates the quintessence scenario only and type II scale factor
generates phantom scenario. But for ECHDE and ECNADE, the both types of scale
factors can accommodate the transition from quintessence to phantom stages
i.e., phantom crossing is possible for entropy corrected terms of HDE and NADE
models. Finally, we show that the models are classically unstable.
