Functions and Analysis

1609 Submissions

[4] viXra:1609.0349 [pdf] replaced on 2016-12-20 11:35:40

Solutions for Euler and Navier-Stokes Equations in Finite and Infinite Series of Time

Authors: Valdir Monteiro dos Santos Godoi
Comments: 22 Pages.

We present solutions for the Euler and Navier-Stokes equations in finite and infinite series of time, in spatial dimension N=3, firstly based on expansion in Taylor’s series of time and then, in special case, solutions for velocity given by irrotational vectors, for incompressible flows and conservative external force, the Bernoulli’s law. A little description of the Lamb’s solution for Euler equations is done.
Category: Functions and Analysis

[3] viXra:1609.0141 [pdf] replaced on 2016-12-27 13:03:54

Solutions for Euler and Navier-Stokes Equations in Powers of Time

Authors: Valdir Monteiro dos Santos Godoi
Comments: 10 Pages.

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.
Category: Functions and Analysis

[2] viXra:1609.0074 [pdf] replaced on 2016-09-27 17:12:07

General Solution For Navier-Stokes Equations With Any Smooth Initial Data

Authors: Valdir Monteiro dos Santos Godoi
Comments: 6 Pages.

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.
Category: Functions and Analysis

[1] viXra:1609.0006 [pdf] replaced on 2017-01-19 09:35:22

Adequate Quaternionic Generalization of Complex Differentiability

Authors: Michael Parfenov
Comments: 46 Pages

The high efficiency of complex analysis is attributable mainly to the ability to represent adequately the Euclidean physical plane essential properties, which have no counterparts on the real axis. In order to provide the similar ability in higher dimensions of space we introduce the general concept of essentially adequate differentiability, which generalizes the key features of the transition from real to complex differentiability. In view of this concept the known Cauchy-Riemann-Fueter equations can be characterized as inessentially adequate. Based on this concept, in addition to the usual complex definition, the quaternionic derivative has to be independent of the method of quaternion division: on the left or on the right. Then we deduce the generalized quaternionic Cauchy-Riemann equations as necessary and sufficient conditions for quaternionic functions to be H-holomorphic. We prove that each H-holomorphic function can be constructed from the C-holomorphic function of the same kind by replacing a complex variable by a quaternionic in an expression for the C-holomorphic function. It follows that the derivatives of all orders of H- holomorphic functions are also H-holomorphic and can be analogously constructed from the corresponding derivatives of C-holomorphic functions. The examples of Liouvillian elementary functions demonstrate the efficiency of the developed theory.
Category: Functions and Analysis