The space $B_{\infty ,\infty }^{-1}$, volumetric sparseness, and 3D NSE

Abstract

In the context of the $L^{\infty }$-theory of the 3D NSE, it is shown that suitable smallness of a solution in Besov space $B_{\infty ,\infty }^{-1}$ suffices to prevent a possible blow-up.

Final version to appear in the Journal of Mathematical Fluid Mechanics (JMFM)

References in corpus (3)

• Lower bounds on the mix norm of passive scalars advected by incompressible enstrophy-constrained flows
• A Lemma and a Conjecture on the Cost of Rearrangements
• Vortex stretching and criticality for the 3D NSE

Cited by in corpus (2)

• Remarks on sparseness and regularity of Navier-Stokes solutions
• Small ${\dot{B}}_{\infty ,\infty }^{-1}$ implies regularity