Mystery solved

How do Japanese schoolgirls keep their socks up at mid-calf, without their socks slipping down?

By using ソックス グルー sokkusu guruu (Socks Glue)!

Apply socks glue (gel-like texture) on your skin and press sock over it. Comes in a compact lipstick-sized tube so that you can carry it in your pocket or put it in your pencilcase for easy re-application.