Godoi, Valdir M.S.
Mathematics and Applied Mathematics
September 12, 2016
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.
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.