Minimal initial data for potential Navier-Stokes singularities

Abstract

Assuming some \dot H^{1/2} - initial data lead to a singularity for the 3d Navier-Stokes equations, we show that there are also initial data with the minimal \dot H^{1/2} - norm which will produce a singularity.

16 pages

References in corpus (2)

• An alternative approach to regularity for the Navier-Stokes equations in critical spaces
• A profile decomposition approach to the $L_t^{\infty }(L_x^3)$ Navier-Stokes regularity criterion

Cited by in corpus (4)

• Profile decompositions for critical Lebesgue and Besov space embeddings
• Uniform stabilization of Navier-Stokes equations in critical $L^q$-based Sobolev and Besov spaces by finite dimensional interior localized feedback controls
• Finite dimensional boundary uniform stabilization of the Boussinesq system in Besov spaces by critical use of Carleman estimate-based inverse theory
• Necessary conditions of potential blow up for Navier-Stokes equations