The Navier-Stokes Existence and Smoothness Poser in ℝⁿ

2015/09/25 by R. K. M. Thambynayagam, Thambynayagam, R. K. Michael
Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1509.08766

openalex publication_date 2015/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we describe a method to derive solutions of the incompressible Navier- Stokes system of equations for non-stationary initial value problems in ℝⁿ. We show that for a given smooth solenoidal initial velocity vector field there exist smooth spatially periodic solutions of pressure and velocity in ℝⁿ. An illustrative example in ℝ³ provides important insights into the ostensible phenomenon of the blowup time.

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