Global existence for two extended Navier-Stokes systems

TL;DR

This paper establishes the global existence of weak solutions for two extended Navier-Stokes systems, broadening the understanding of viscous flow dynamics under less regular domain conditions.

Contribution

It introduces a novel approach to prove weak solution existence for extended Navier-Stokes systems in less regular domains, including addressing uniqueness in 2D.

Findings

Proves global existence of weak solutions for extended Navier-Stokes systems.

Addresses existence in domains with less than C^1 regularity.

Provides results on uniqueness in 2D and higher regularity cases.

Abstract

We prove global existence of weak solutions to two systems of equations which extend the dynamics of the Navier-Stokes equations for incompressible viscous flow with no-slip boundary condition. The systems of equations we consider arise as formal limits of time discrete pressure-Poisson schemes introduced by Johnston and Liu (J. Comp. Phys. 199 (2004) 221-259) and by Shirokoff and Rosales (J Comp. Phys 230 (2011) 8619-8646) when the initial data does not satisfy the required compatibility condition. Unlike the results of Iyer et al (J. Math. Phys. 53 (2012) 115605), our approach proves existence of weak solutions in domains with less than C^1 regularity. Our approach also addresses uniqueness in 2D and higher regularity.