caa a22 4500 605523592 CHVBK 20210128100750.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s10958-015-2593-0 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2593-0 Repin S. St.Petersburg Department of the Steklov Mathematical Institute, State Polytechnical University, St.Petersburg, Russia aut Estimates of the Distance to the Set of Divergence Free Fields [Elektronische Daten] [S. Repin] The paper deals with computable estimates of the distance to the set of divergence free fields, which are necessary for quantitative analysis of mathematical models of incompressible media (e.g., the Stokes, Oseen, and Navier-Stokes problems). The distance is measured in terms of the L q norm of the gradient with q ∈ (1,+∞). For q = 2, these estimates follow from the so-called inf-sup condition (or the Aziz-Babuška-Ladyzhenskaya-Solonnikov inequality) and require sharp estimates of the respective constant, which are known only for a very limited amount of cases. A way to bypass this difficulty is suggested, and it is shown that for a wide class of domains (and different boundary conditions), the computable estimates of the distance to the set of divergence free fields can be presented in the form, which uses inf-sup constants for certain basic problems. In the last section, these estimates are applied to problems in the theory of viscous incompressible fluids. They generate fully computable bounds of the distance to generalized solutions of the problems considered. Bibliography: 26 titles. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 210/6(2015-11-01), 822-834 1072-3374 210:6<822 2015 210 10958 https://doi.org/10.1007/s10958-015-2593-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2593-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Repin S. St.Petersburg Department of the Steklov Mathematical Institute, State Polytechnical University, St.Petersburg, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 210/6(2015-11-01), 822-834 1072-3374 210:6<822 2015 210 10958