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Modeling of the unsteady flow through a channel with an artificial outflow condition by the Navier–Stokes variational inequality
Author(s) -
Kračmar Stanislav,
Neustupa Jiří
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700228
Subject(s) - mathematics , outflow , boundary (topology) , boundary value problem , variational inequality , flow (mathematics) , regular polygon , nothing , mathematical analysis , type (biology) , navier–stokes equations , series (stratigraphy) , geometry , mechanics , physics , meteorology , compressibility , ecology , philosophy , paleontology , epistemology , biology
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.