This is the 5th generation of popular Asics Gel Rocket line of shoes.
The Gel Rocket 5 Asics are available in blue and white like this:
They’re also available in this swell color scheme, which Asics calls White / Onyx / Silver:
Onyx? Just for reference, here’s a kitchen countertop made out of onyx:
Looks like there’s also this grey guy:
Image via prospin.com.br
And a black version: