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)|
|Number of pages||14|
|Journal||Archive for Rational Mechanics and Analysis|
|State||Published - Dec 30 2015|
ASJC Scopus subject areas
- Mathematics (miscellaneous)
- Mechanical Engineering