A global solution for the tαtα-type Navier–Stokes equations

In the present paper, the special type of Navier–Stokes equations (1.1) is investigated. The viscosity varies according to tαtα, and we call it the tαtα-type Navier–Stokes equation. By using the fixed point theorem in special Besov spaces, the global existence and uniqueness results of the solution for 0≤α<10≤α<1 are given under the assumption of small initial data.