Related papers: A Dynamic alpha Model for the Lagrangian Averaged …

This paper has been withdrawn.

This paper has been withdrawn by the author due to a coming paper completely superseding it.

In this paper statistical solutions of the 3D Navier-Stokes-$\alpha$ model with periodic boundary condition are considered. It is proved that under certain natural conditions statistical solutions of the 3D Navier-Stokes-$\alpha$ model…

The article `Global regularity for the 3D Navier-Stokes and the 3D Euler equations'(arXiv:0711.2453) is withdrawn due to a serious error in the proof.

This paper has been withdrawn by the authors because it has been merged with paper arXiv:0903.3501v1 [math.DG]

This paper has been withdrawn by the authors due to a gap in the proof of the main result (in 5.3).

The primary emphasis of this work is the development of a finite element based space-time discretization for solving the stochastic Lagrangian averaged Navier-Stokes (LANS-$\alpha$) equations of incompressible fluid turbulence with…

This paper has been withdrawn by the author. A revised and expanded version is gr-qc/9907028 (Phys.Rev. D60 (1999) 104043).

This paper has been withdrawn by the author. The most updated version can be accessed by arXiv:1806.07290.

This paper has been withdrawn by the author due to the unsure solution to the Dyson-Schwinger equation.

This paper was withdrawn by the authors.

We show that the Navier-Stokes as well as a random perturbation of this equation can be derived from a stochastic variational principle where the pressure is introduced as a Lagrange multiplier. Moreover we describe how to obtain…

This paper has been retracted.

This paper has been withdrawn by the authors.

This paper has been withdrawn by the authors because the paper is largely revised and improved, and to appear in Mechanics Research Communications.

This paper has been withdrawn

This paper has been withdrawn by the author

This paper has been withdrawn

This paper has been withdrawn by the authors due to inadequate arguments.

This paper has been withdrawn by the author [arXiv admin].