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Coercivity and stability results for an extended Navier-Stokes system

journal contribution
posted on 2023-06-08, 17:20 authored by Gautam Iyer, Robert L Pego, Arghir Zarnescu
In this paper, we study a system of equations that is known to extend Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role of divergence and pressure in developing energy estimates capable of both controlling the nonlinear terms, and being useful at the time-discrete level. We address questions of global existence and stability in bounded domains with no-slip boundary conditions. Through use of new H^1 coercivity estimates for the linear equations, we establish a number of global existence and stability results, including results for small divergence and a time-discrete scheme. We also prove global existence in 2D for any initial data, provided sufficient divergence damping is included.

History

Publication status

  • Published

Journal

Journal of Mathematical Physics

ISSN

0022-2488

Publisher

American Institute of Physics

Volume

53

Page range

115605

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2014-08-07

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