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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 ZarnescuIn 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.
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Publication status
- Published
Journal
Journal of Mathematical PhysicsISSN
0022-2488Publisher
American Institute of PhysicsExternal DOI
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53Page range
115605Department affiliated with
- Mathematics Publications
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- No
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- Yes
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2014-08-07Usage metrics
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