Strichartz estimates for homogeneous repulsive potentials

The homogeneous repulsive potentials accelerate a quantum particle and the velocity of the particle increases exponentially in $t$; this phenomenon yields the fast decaying dispersive estimates and hence we consider the Strichartz estimates associated with this phenomenon. First, we consider the free repulsive Hamiltonian and prove that the Strichartz estimates hold for every admissible pairs $(q,r)$, which satisfy $1/q +n/(2r) \geq n/4$ with $q$, $r \geq 2$. Second, we consider the perturbed repulsive Hamiltonian with the slowly decaying potential such that $|V(x)| \leq C(1+|x|)^{-\delta}$ for some $\delta >0$, and prove the Strichartz estimate with the same admissible pairs for the free case.