Phantom dark energy models with negative kinetic term

We examine phantom dark energy models derived from a scalar field with a negative kinetic term for which V () asymptotically. All such models can be divided into three classes, corresponding to an equation of state parameter w_ with asymptotic behavior w_-1, w_w₀<-1, and w_-. We derive the conditions on the potential V () which lead to each of these three types of behavior. For models with w_-1, we derive the conditions on V () which determine whether or not such models produce a future big rip. Observational constraints are derived on two classes of these models: power-law potentials with V () =^ (with positive or negative) and exponential potentials of the form V () =e^{^}. It is shown that these models spend more time in a state with ₌_ than do corresponding models with a constant value of w_, thus providing a more satisfactory solution to the coincidence problem.