Modeling of the unsteady flow through a channel with an artificial outflow condition by the Navier-Stokes variational inequality

0492103 - MÚ 2019 RIV DE eng J - Journal Article
Kračmar, Stanislav - Neustupa, Jiří
Modeling of the unsteady flow through a channel with an artificial outflow condition by the Navier-Stokes variational inequality.
Mathematische Nachrichten. Roč. 291, 11-12 (2018), s. 1801-1814. ISSN 0025-584X. E-ISSN 1522-2616
R&D Projects: GA ČR GA16-03230S
Institutional support: RVO:67985840
Keywords : do nothing outflow boundary conditions * Navier-Stokes equation * variational inequality
OECD category: Pure mathematics
Impact factor: 0.847, year: 2018
https://onlinelibrary.wiley.com/doi/abs/10.1002/mana.201700228

We prove the global in time existence of a weak solution to the variational inequality of the Navier-Stokes type, simulating the unsteady flow of a viscous fluid through the channel, with the so-called 'do nothing' boundary condition on the outflow. The condition that the solution lies in a certain given, however arbitrarily large, convex set and the use of the variational inequality enables us to derive an energy-type estimate of the solution. We also discuss the use of a series of other possible outflow 'do nothing' boundary conditions.
Permanent Link: http://hdl.handle.net/11104/0285665