Application of Analytic Functions to the Global Solvabilty of the Cauchy Problem for Equations of Viscous Incompressible Liquid

TL;DR

This paper explores how analytic functions can be used to develop new estimation methods for solving the Cauchy problem related to equations of viscous incompressible liquids, linking complex analysis with fluid dynamics.

Contribution

It introduces a novel approach using analytic functions to improve estimation techniques for the Cauchy problem in viscous incompressible fluid equations.

Findings

New estimation methods for the Cauchy problem developed.

Analytic functions provide nonlinear representations aiding in problem solving.

Methods validated through application to viscous incompressible liquid equations.

Abstract

The interrelation between analytic functions and real-valued functions is formulated in the work. It is shown such an interrelation realizes nonlinear representations for real-valued functions that allows to develop new methods of estimation for them. These methods of estimation are approved by solving the Cauchy problem for equations of viscous incompressible liquid.