Global solution of the 3D incompressible Navier-Stokes equations in the Besov spaces (R) over dot r1,r2,r3σ,1

In this paper, we construct a more general Besov spaces (R) over dot(r1,r2,r3)(sigma,q) and consider the global well-posedness of incompressible Navier-Stokes equations with small data in (R) over dot(r1,r2,r3)(sigma,1) for 1/r(1) + 1/r(2) + 1/r(3) = - sigma = 1, 1 < r(i) < infinity and max(1 <= i <= 3) r(i) <= 2 min(1 <= i <= 3) r(i). In particular, by studying the well-posedness of incompressible Navier-Stokes equations in (R) over dot(r1,r2,r3)(sigma,1), we can explore the relationship between u(1)(x, t), u(2)(x, t) and u(3)(x, t) in u(x, t).