English

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

Analysis of PDEs 2024-12-10 v4 Complex Variables Functional Analysis

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.

Keywords

Cite

@article{arxiv.2405.07929,
  title  = {On the Existence and Smoothness of the Navier-Stokes Equation I},
  author = {Brian David Vasquez Campos},
  journal= {arXiv preprint arXiv:2405.07929},
  year   = {2024}
}