Structure of Helicity and Global Solutions of Incompressible Navier–Stokes Equation
- 842 Downloads
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.
KeywordsInitial Data Stokes Equation Global Solution Smooth Solution Global Regularity
Unable to display preview. Download preview PDF.
- 3.Fefferman, C.L.: http://www.claymath.org/millennium/Navier-Stokes_Equations/. Accessed 1 May 2000
- 4.Hou, T., Lei, Z., Li, Congming: global regularity of the three-dimensional axi-symmetric Navier–Stokes equations with anisotropic data. Comm. Partial Differ. Equ., 33(7–9), 1622–1637 (2008)Google Scholar
- 5.Ladyzhenskaya, O.A.: Unique global solvability of the three-dimensional Cauchy problem for the Navier–Stokes equations in the presence of axial symmetry, Zap. Naucn. Sem. Leningrad. Otdel. Math. Inst. Steklov. (LOMI), 7, 155–177 (1968). (Russian) Google Scholar
- 6.Majda, A., Bertozzi, A.: Vorticity and Incompressible Flow. Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2002Google Scholar