  The so-called Einstein-Aether theory is General Relativity coupled (at second
derivative order) to a dynamical unit time-like vector field (the aether). It
is a Lorentz-violating theory, and gained much attention in the recent years.
In the present work, we study the cosmological evolution of Einstein-Aether
models with power-law-like potential, by using the method of dynamical system.
In the case without matter, there are two attractors which correspond to an
inflationary universe in the early epoch, or a de Sitter universe in the late
time. In the case with matter but there is no interaction between dark energy
and matter, there are only two de Sitter attractors, and no scaling attractor
exists. So, it is difficult to alleviate the cosmological coincidence problem.
Therefore, we then allow the interaction between dark energy and matter. In
this case, several scaling attractors can exist under some complicated
conditions, and hence the cosmological coincidence problem could be alleviated.
