title: Optimal control of the Navier— Stokes system with a space variable in a network-like domain
metadata.name: dc.contributor.author
metadata.value: Zhabko, Aleksei P.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Provotorov, Vyacheslav V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Sergeev, Sergey M.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-02-19T14:08:25Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-02-19T14:08:25Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Zhabko A. P., Provotorov V. V., Sergeev S. M. Optimal control of the Navier— Stokes system with a space variable in a network-like domain. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2023, vol. 19, iss. 4, pp. 549–562. https://doi.org/10.21638/11701/spbu10.2023.411
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2023.411
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/44912
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The research of the problem of optimal control of the Navier—Stokes evolutionary differential
  system, considered in Sobolev spaces, the elements of which are functions with carriers
  in an n-dimensional network-like domain, is presented. Such domain consists of a finite
  number of subdomains, mutually adjacent to certain parts of the surfaces of their boundaries
  according to the graph type. For functions that are elements of these spaces, the conditions
  for the existence of traces on the surfaces of the joining are presented and the conditions of
  adjacency subdomains to which these functions satisfy are described. In applied questions of
  the analysis of the processes of transport of continuous media, the conditions of adjacency
  describe the regularities of the flow of fluid through the boundaries of the adjacent domains.
  The paper presents the results of following main research questions: 1) weak solvability
  of the initial boundary value problem for the Navier—Stokes system and obtaining the
  conditions for the existence of a weak solution to this problem; 2) the formation and solution
  of optimal control problems of various types of Navier—Stokes system. The fundamental
  approach to the analysis of the weak solvability of the initial boundary value problem is its
  reduction to the differential-difference problem (semi-digitization of the original system by
  a time variable) and subsequent use of a priori estimates for weak solutions of the obtained
  boundary value problems. The obtained a priori estimates are used to prove the theorem of
  the existence of a weak solution of the original differential system and indicate the way of the
  actual construction of this solution. A universal approach to solving the problems of optimal
  distributed and starting control of the Navier—Stokes evolutionary system is presented. The
  latter essentially expands the possibilities of analyzing non-stationary network-like processes
  of applied hydrodynamics (for example, processes of transporting various types of liquids
  through network or main line pipelines) and optimal control of these processes.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 19; Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: differential-difference system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: evolutionary Navier—Stokes system
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: network-like domain
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: solvability
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: optimal control
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Optimal control of the Navier— Stokes system with a space variable in a network-like domain
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 11.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/44912/1/11.pdf
resources.format: Adobe PDF
resources.size: 260,86 kB