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 - May 21 2015

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Incompressible Navier-Stokes
Helicity
Global Solution
Navier-Stokes Equations
Smooth Solution
Energy Functional
Energy
Scaling
Norm
Three-dimensional

ASJC Scopus subject areas

  • Analysis
  • Mechanical Engineering
  • Mathematics (miscellaneous)

Cite this

Structure of Helicity and Global Solutions of Incompressible Navier–Stokes Equation. / Lei, Zhen; Lin, Fang-Hua; Zhou, Yi.

In: Archive for Rational Mechanics and Analysis, Vol. 218, No. 3, 21.05.2015, p. 1417-1430.

Research output: Contribution to journalArticle

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