A solution to the incompressible Navier-Stokes Equation

TL;DR

This paper presents a power series solution for the incompressible Navier-Stokes equations in multiple dimensions, proving global convergence and thus addressing the existence and smoothness problem.

Contribution

It introduces a convergent power series method for solving the Navier-Stokes equations, providing a new approach to the longstanding existence and smoothness problem.

Findings

Solution expressed as a power series in time with known coefficients

Proves global convergence of the solution series

Addresses the existence and smoothness problem for the equations

Abstract

For the N>=2 dimensional incompressible Naver-Stokes Equation, We have got its solution as a power series of time t, in which the coefficients are all known functions determined only by the initial velocity v0. We also prove that the solution series is convergent globally, so that the existence and smoothness problem are solved.