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 in the picture above.
Buy (US): amazon.com
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: