## New Equations of the Resolution of The Navier-Stokes Equations

**Authors:** Abdelmajid Ben Hadj Salem

This paper represents an attempt to give a solution of the Navier-Stokes equations under the assumptions (A) of the problem as described by the Clay Mathematics Institute. After elimination of the pressure, we obtain the fundamental equations function of the velocity vector u and vorticity vector \Omega=curl(u), then we deduce the new equations for the description of the motion of viscous incompressible fluids, derived from the Navier-Stokes equations, given by:
\nu \Delta \Omega -\frac{\partial \Omega}{\partial t}=0
\Delta p=-\sum^{i=3}_{i=1}\sum^{j=3}_{j=1}\frac{\partial u_i}{\partial x_j}\frac{\partial u_j}{\partial x_i}
Then, we give a proof of the solution of the Navier-Stokes equations u and p that are smooth functions and u verifies the condition of bounded energy.

**Comments:** 14 Pages. Submitted to the journal Annals of PDE. Comments welcome.

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### Submission history

[v1] 2018-12-19 12:39:47

[v2] 2018-12-20 08:27:21

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