Existence and uniqueness of solutions for Navier–Stokes equations with hyper-dissipation in a large space

We study Cauchy problem of the 3D Navier–Stokes equations with hyper-dissipation. By using the Fourier localization technique, we prove that the system has a unique global solution for large initial data in a critical Fourier–Herz space. More importantly, the energy of this solution is infinite.