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Global existence for two extended Navier-Stokes systems

journal contribution
posted on 2023-06-08, 20:19 authored by Mihaela Ignatova, Gautam Iyer, James P Kelliher, Robert L Pego, Arghir D Zarnescu
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 \& Liu {[}J. Comput. Phys. 199, 221-259, 20041 and by Shirokoff \& Rosales {[}J. Comput. Phys. 230, 8619-8646, 20111 when the initial data does not satisfy the required compatibility condition. Unlike the results of Iyer et al. {[}J. Math. Phys. 53, 115605, 20121, our approach proves existence of weak solutions in domains with less than regularity. Our approach also addresses uniqueness in 2D and higher regularity.

History

Publication status

  • Published

Journal

Communications in Mathematical Sciences

ISSN

1539-6746

Publisher

International Press

Issue

1

Volume

13

Page range

249-267

Place of publication

PO BOX 43502, SOMERVILLE, MA 02143 USA

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2015-03-13

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