Optimal feedback control for alpha-Leray model and for alpha-Navier-Stokes model

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

The existence of optimal feedback control for the alpha-Leray model and for the alpha-Navier-Stokes model are proved. The existence of an optimal solution yielding the minimum of a specified bounded lower semicontinuous quality functional is obtained. To establish the existence of an optimal solution, the topological approximation method for studying problems of hydrodynamics is used.

About the authors

А. V. Zvyagin

Voronezh State University

Author for correspondence.
Email: zvyagin@mail.ru
Russian Federation, 1, University square, Voronezh, 394063

References

  1. Lemarie-Rieusset P.G. // The Naviez-Stokes Problem in the 21st Century. CRC Press / Taylor and Francis Group, 2016.
  2. Cheskidov В. В., Holm D. D., Olson E., Titi E. S. // Proc. Roy. Soc. London. Ser. A Math. Phys. Eng. Sci. 2005. V. 461. P. 629-649.
  3. Звягин А. В. // Изв. вузов. Мат. 2016. № 10. С. 70-75.
  4. Foias C., Holm D. D., Titi E. S. // J. Dyn. Different. Equat. 2002. V. 14. N. 1. P. 1-35.
  5. Zvyagin V., Obukhovskii V., Zvyagin A. // JFPTA. 2014. V. 16. P. 27-82.
  6. Zvyagin V. G., Turbin M. V. // JOTA. 2011. V. 148. P. 146-163.
  7. Фурсиков А. В. Оптимальное управление распределёнными системами. Новосибирск: Научн. кн., 1999.
  8. Звягин В. Г., Турбин М. В. Математические вопросы гидродинамики вязкоупругих сред. М.: КРАСАНД УРСС, 2012.
  9. Zvyagin V. G. // J. Math. Sci. 2014. V. 201. P. 830-858.
  10. Звягин А. В. // ДАН. 2016. Т. 468. № 3. С. 251-253.
  11. Звягин А. В. // Диференц. уравнения. 2013. Т. 49. № 2. С. 245-249.
  12. Звягин А В. // Сиб. мат. журн. 2013. Т. 54. № 4. С. 807-825.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2019 Russian academy of sciences