Trotter product formulas and global regular upper bounds of the Navier Stokes equation solution

TL;DR

This paper develops a novel infinite scheme using Trotter product formulas with infinitesimal errors to establish global regular upper bounds for solutions of the incompressible Navier-Stokes equations, enhancing understanding of their regularity.

Contribution

It introduces a new infinite scheme employing Trotter product formulas with explicit infinitesimals to derive global regular bounds for Navier-Stokes solutions.

Findings

Constructed global upper bounds for Navier-Stokes solutions

Derived Trotter product formulas with infinitesimal error

Simplified the analysis of spatial effects in regularity proofs

Abstract

Global upper bounds with respect to regular norms of the incompressible Navier Stokes equation solution with regular data are constructed by an infinite scheme, where we work in bounded ZFC with bounded quantifiers and explicit infinitesimals. Trotter product formulas with infinitesimal error are obtained, which simplify for calculi with explicit infinitesimal and make the spatial effects needed in order to obtain global schemes more transparent.