Spherical averaged endpoint strichartz estimates for the two-dimensional schr?dinger equation with inverse square potential

摘要

We investigate the two-dimensional Schr?dinger equation with repulsive inverse square potential, and we prove the following homogeneous endpoint Strichartz estimate: ∥u∥L_t~2(L_r~∞ L_θ ≤ C par;u0∥L~2 where L_r~∞ L_θ is a norm that applies L~2 average on the angular variable, first, and then the supremum on the radial variable.