Functions and Analysis

    

Existence and Smoothness of Solutions to the Navier-Stokes Equations Using Fourier Series Representation

Authors: Biruk Alemayehu Petros

This paper presents an analytic solution to the Navier-Stokes equations for incompressible fluid flow with a periodic initial velocity vectorfield. Leveraging Fourier series representations, the velocity fields are expressed as expansions, accounting for their temporal evolution. Thesolution’s existence and smoothness are verified by demonstrating its consistency with the Navier-Stokes equations, including the incompressibilitycondition and pressure compatibility. The proposed solution contributes to understanding fluid dynamics and offers insights into the millennium prize problem related to the Navier-Stokes equations. This work lays the groundwork for further investigations into fluid flow behavior under various conditions and geometries, combininganalytical and numerical approaches to advance our understanding of fluid dynamics.

Comments: 11 Pages. This is continuation of published result.

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Submission history

[v1] 2024-06-09 03:31:05

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