Structure of Helicity and Global Solutions of Incompressible Navier–Stokes Equation

Zhen Lei, Fang Hua Lin, Yi Zhou

Research output: Contribution to journalArticle

Abstract

In this paper we derive a new energy identity for the three-dimensional incompressible Navier–Stokes equations by a special structure of helicity. The new energy functional is critical with respect to the natural scalings of the Navier–Stokes equations. Moreover, it is conditionally coercive. As an application we construct a family of finite energy smooth solutions to the Navier–Stokes equations whose critical norms can be arbitrarily large.

Original languageEnglish (US)
Pages (from-to)1417-1430
Number of pages14
JournalArchive for Rational Mechanics and Analysis
Volume218
Issue number3
DOIs
StatePublished - Dec 30 2015

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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