Solving some Navier-Stokes Equations with the initial conditions being some complex-valued periodic functions on $R^3$

TL;DR

This paper presents a novel iterative approach using series expansions to solve certain Navier-Stokes equations with complex-valued periodic initial conditions, and proposes a new strategy related to the Navier-Stokes conjecture.

Contribution

Introduces a new iterative method and series-based approach for solving Navier-Stokes equations with complex initial data, offering insights into the conjecture.

Findings

Successful application of series and iterative methods to specific Navier-Stokes problems

Proposed a new strategy for addressing the Navier-Stokes conjecture

Provides potential pathways for future analytical or numerical solutions

Abstract

In this paper, we utilize some series and an iterative method to solve some Navier-Stokes equations with the initial conditions being some complex-valued periodic functions on $R^3$. Then a new strategy for dealing with the conjecture of the Navier-Stokes equation is given.