We study the well-posedness and regularity of the generalized Navier-Stokes equations with initial data in a new critical space Qα;∞ β,-1(R{double-struck}n)=Δ·(Qα β(R{double-struck}n))n, β∈(1/2,1), which is larger than some known critical homogeneous Besov spaces. Here Qα; ∞ β(R{double-struck}n) is a space defined as the set of all measurable functions with. sup(l(I))2(α+β-1)-n∫I∫I|f(x)-f(y)|2/|x-y|n+2(α-β+1)dxdy<∞ where the supremum is taken over all cubes I with edge length l(I) and edges parallel to the coordinate axes in R{double-struck}n. In order to study the well-posedness and regularity, we give a Carleson measure characterization of Qα β(R{double-struck}n) by investigating a new type of tent spaces and an atomic decomposition of the predual for Qα β(R{double-struck}n). In addition, our regularity results apply to the incompressible Navier-Stokes equations with initial data in Qα;infin; 1,-1(R{double-struck}n). © 2010 Elsevier Inc.