An effective approach to the solution of a system of nonlinear differential equations in partial derivatives

TL;DR

This paper introduces a new approach for solving systems of nonlinear partial differential equations, demonstrated on the Navier-Stokes equations, with potential applications to other complex systems.

Contribution

The paper presents a novel method for solving nonlinear PDE systems, inspired by solutions to the 3D Navier-Stokes equations, expanding the toolkit for such challenging problems.

Findings

Successfully applied to Navier-Stokes equations

Potential applicability to other nonlinear PDE systems

Provides detailed solution methodology

Abstract

There are few approaches to the solution of a system of nonlinear differential equations in partial derivatives, for example $\cite{NK87} - \cite{EK98}$. In our paper we propose an approach that was used to solve the Navier-Stokes equations in three dimensional space. This solution is described in details in article "Existence, uniqueness and smoothness of solution for 3D Navier-Stokes equations with any smooth initial velocity" $\cite{TT12}$. The authors expect that it can be successfully applied to other systems of nonlinear differential equations in partial derivatives.