Functions and Analysis

2606 Submissions

[3] viXra:2606.0035 [pdf] submitted on 2026-06-10 10:49:40

Elementary Weak Solutions of the Navier—Stokes Equations and an Application of the Banach Fixed-Point Theorem

Authors: Masatoshi Ohrui
Comments: 23 Pages.

This is an application of functional analysis to the existence and smoothness of the Navier—Stokes equations using elementary weak solutions in Sobolev spaces.We solve the problem in mathematics. The problems are not in physics, so we do not use any physics or assumptions-falsified mathematics, such as other papers. We use mathematics only. We can solve the problem by using an exactly and completely FALSIFIED resolution, where large initial values destroy the earth, because uniqueness does NOT hold, or SMALL initial values love your cup of coffee.There are no long or complicated calculations; semi-groups, a priori estimates, and boundary conditions are not used at all. We apply the local solvability of linear partial differential operators with constant coeficients.
Category: Functions and Analysis

[2] viXra:2606.0034 [pdf] submitted on 2026-06-10 10:55:32

Proof of Hartog’s Phenomenon and Cohomology Vanishing Theorem

Authors: Masatoshi Ohrui
Comments: 2 Pages.

We can prove Hartog’s phenomenon by solving the ∂-bar equation for compactly supported forms. To solve the equation, we construct the solution using convolution.
Category: Functions and Analysis

[1] viXra:2606.0017 [pdf] submitted on 2026-06-06 18:49:02

Hastings-Cody Approximations of the Integral of a Power Times the Complete Elliptic Integral of the First Kind

Authors: Richard J. Mathar
Comments: 16 Pages.

Hastings and later Cody tabulated minimax polynomial approximations for the Complete Elliptic Integral of the First Kind. The simplicity of this representation by polynomials and polynomials times a logarithm allows to integrate their terms analytically. We demonstrate how integrals of the Complete Elliptic Integral times a power of its argument achieve double precision accuracy for powers from 0 to 2 based on Cody's polynomials up to 9th order.
Category: Functions and Analysis