Here we denote
and
Wasserstein-2 AIG flow is also derived in [1, 2].
[1] José A Carrillo, Young-Pil Choi, and Oliver Tse. Convergence to equilibrium in Wasserstein distance for damped Euler equations with interaction forces. Communications in Mathematical Physics, 365(1):329–361, 2019.
[2] Amirhossein Taghvaei and Prashant G Mehta. Accelerated flow for probability distributions. arXiv preprint arXiv:1901.03317, 2019.