Sturmian Multiple Zeros for Stokes and Navier--Stokes Equations in $\re^3$ via Solenoidal Hermite Polynomials

TL;DR

This paper investigates the formation of multiple zeros in solutions to the Stokes and Navier-Stokes equations in three dimensions, linking these phenomena to solenoidal Hermite polynomials and extending the analysis to Burnett equations.

Contribution

It introduces a novel connection between zero formations in fluid equations and solenoidal Hermite polynomials, extending the analysis to Burnett equations with bi-harmonic viscosity.

Findings

Multiple zero formations are characterized by nodal sets of solenoidal Hermite polynomials.

Extensions to Burnett equations with bi-harmonic viscosity are discussed.

The study provides a new mathematical framework for understanding zero structures in fluid dynamics.

Abstract

Multiple spatial zero formations for Stokes and Navier-Stokes equations in three dimensions are shown to occur according to nodal sets of solenoidal Hermite polynomials. Extensions to well-posed Burnett equations with the bi-harmonic viscosity operator are also discussed.