**Author:**

Godoi, Valdir M.S.

**Category:**

Research Papers

**Sub-Category:**

Mathematics and Applied Mathematics

**Date Published:**

September 12, 2016

**Keywords:**

Lagrange, Mécanique Analitique, exact differential, Euler’s equations, Navier-Stokes equations, Taylor’s series, Cauchy, Mémoire sur la Théorie des Ondes, Lagrange’s theorem, Bernouilli’s law.

**Abstract:**

We present a solution for the Navier-Stokes equations for incompressible case with any smooth (C^∞) initial velocity given a pressure and external force in n = 3 spatial dimensions, based on expansion in Taylor’s series of time. Without major difficulties, it can be adapted to any spatial dimension, n≥1.

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