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

Zhen Lei; Fang Hua Lin; Yi Zhou

doi:10.1007/s00205-015-0884-8

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

Zhen Lei, Fang Hua Lin, Yi Zhou

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	1417-1430
Number of pages	14
Journal	Archive for Rational Mechanics and Analysis
Volume	218
Issue number	3
DOIs	https://doi.org/10.1007/s00205-015-0884-8
State	Published - Dec 30 2015

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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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.",

author = "Zhen Lei and Lin, {Fang Hua} and Yi Zhou",

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AB - 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.

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

Abstract

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