# Science at the triple point between mathematics, mechanics and materials science

## Publication 101

### Global existence for two extended Navier-Stokes systems

##### Authors:

Mihaela Ignatova

Gautam Iyer
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

James P. Kelliher

Robert L. Pego
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

Arghir Zarnescu
Department of Mathematics
University of Sussex
Pevensey III, Falmer, BN1 9QH, United Kingdom

##### 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.
##### Get the paper in its entirety
13-CNA-017.pdf

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