On the Existence and Smoothness of the Navier-Stokes Equation I

2024/05/13 by Brian David Vasquez Campos, Campos, Brian David Vasquez
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Heat Transfer and Mathematical Modeling #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2405.07929

openalex publication_date 2024/05/13 · openalex created_date 2024/05/15 · openalex updated_date 2026/07/28

Abstract

In this paper, we give a sufficient condition to guarantee the existence of a smooth solution of the Navier-Stokes Equation with the nice decreasing properties at infinity. In this way, we prove the existence of smooth physically reasonable solutions to the Navier-Stokes problem. Additionally, we show the existence of a smooth curve of entire vector fields of order 2 that extends the solution to the complex domain for positive time.

Related

• Existence of Smooth Solutions of the Navier-Stokes Equations
• Existence and Smoothness of Navier-Stokes Equations
• The existence and uniqueness of the smoothing solution of the Navier-Stokes equations
• Smooth Solutions of the Navier-Stokes Equation
• The global existence of the smoothing solution for the Navier-Stokes equations