Asymptotic stability of explicit infinite energy blowup solutions of the 3D incompressible Navier-Stokes equations

In this paper, we study the dynamical stability of a family of explicit blowup solutions of the three-dimensional (3D) incompressible Navier-Stokes (NS) equations with smooth initial values, which is constructed in Guo et al. (2008). This family of solutions has finite energy in any bounded domain of ℝ 3 , but unbounded energy in ℝ 3 . Based on similarity coordinates, energy estimates and the Nash-Moser-Hörmander iteration scheme, we show that these solutions are asymptotically stable in the backward light-cone of the singularity. Furthermore, the result shows the existence of local energy blowup solutions to the 3D incompressible NS equations with growing data. Finally, the result also shows that in the absence of physical boundaries, the viscous vanishing limit of the solutions does not satisfy the 3D incompressible Euler equations.