**Author:**

Godoi, Valdir M.S.

**Category:**

Research Papers

**Sub-Category:**

Mathematical Physics

**Date Published:**

December 23, 2015

**Keywords:**

Navier-Stokes equations, Euler equations, continuity equation, breakdown, existence, smoothness, solutions, gradient field, conservative field, velocity, pressure, external force, millenium problem

**Abstract:**

We have proved that there are initial velocities

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