Archive for Rational Mechanics and Analysis

, Volume 218, Issue 3, pp 1417–1430 | Cite as

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

  • Zhen LeiEmail author
  • Fang-Hua Lin
  • Yi Zhou


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.


Initial Data Stokes Equation Global Solution Smooth Solution Global Regularity 
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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Mathematical Sciences (and SCMC, LMNS and SKLCAM)Fudan UniversityShanghaiPeople’s Republic of China
  2. 2.Courant Institute of MathematicsNew York UniversityNew YorkUSA
  3. 3.Institute of Mathematical SciencesECNU, NYUShanghaiPeople’s Republic of China

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