Affine Variant of Fractional Sobolev Space with Application to Navier-Stokes System

الأصل · EN

It is proved that for α∈ (0,1), Qα(), not only as an intermediate space of W¹,ⁿ() and BMO() but also as an affine variant of Sobolev space L²α() which is sharply imbedded in L²ⁿ/ⁿ⁻²α(), is isomorphic to a quadratic Morrey space under fractional differentiation. At the same time, the dot product ∇·(Qα())ⁿ is applied to derive the well-posedness of the scaling invariant mild solutions of the incompressible Navier-Stokes system in =(0,∞)×.