On weak–strong uniqueness of solutions to the generalized incompressible Navier–Stokes equations

In the recent paper Li and Zhai (2010) proved the well-posedness of the Cauchy problem to the nn-dimensional generalized incompressible Navier–Stokes equations with initial data u0u0 ​belonging to the so-called QQ-space Qα;∞β,−1(Rn) with β∈(12,1] and α∈[0,β)α∈[0,β). In this paper, by using the Littlewood–Paley theory, we prove the weak–strong uniqueness between weak solution and Li–Zhai’s strong solution for the nn-dimensional generalized incompressible Navier–Stokes equations.