Global Solution for the Generalized Anisotropic Navier–Stokes Equations with Large Data

Abstract

We are concerned with 3D incompressible generalized anisotropic Navier– Stokes equations with hyperdissipative term in horizontal variables. We prove that there exists a unique global solution for it with large initial data in anisotropic Besov space.

Keywords:

• anisotropic
• hyper-dissipation
• large data

AMS Subject Classification:

• 35Q30
• 35Q35
• 76D03