Valdir Monteiro dos Santos Godoi
Abstract
We present a solution for the Euler and Navier-Stokes equations for incompressible case given any smooth (C^∞) initial velocity, 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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We present a solution for the Euler and Navier-Stokes equations for incompressible case given any smooth (C^∞) initial velocity, 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.
Key concepts: Euler equations, Dimension (graph theory), Euler's formula, Compressibility, Semi-implicit Euler method, Mathematical analysis, Mathematics, Series (stratigraphy)