Higher derivatives estimate for the 3D Navier–Stokes equation

  • Alexis Vasseur

    Department of Mathematics, University of Texas, 1 University Station C 1200, Austin, TX, United States

Abstract

In this article, a nonlinear family of spaces, based on the energy dissipation, is introduced. This family bridges an energy space (containing weak solutions to Navier–Stokes equation) to a critical space (invariant through the canonical scaling of the Navier–Stokes equation). This family is used to get uniform estimates on higher derivatives to solutions to the 3D Navier–Stokes equations. Those estimates are uniform, up to the possible blowing-up time. The proof uses blow-up techniques. Estimates can be obtained by this means thanks to the galilean invariance of the transport part of the equation.

Cite this article

Alexis Vasseur, Higher derivatives estimate for the 3D Navier–Stokes equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 5, pp. 1189–1204

DOI 10.1016/J.ANIHPC.2010.05.002