Email this article Optimal feedback control for alpha-Leray model and for alpha-Navier-Stokes model
- Authors: Zvyagin А.V.1
-
Affiliations:
- Voronezh State University
- Issue: Vol 486, No 5 (2019)
- Pages: 527-530
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/14469
- DOI: https://doi.org/10.31857/S0869-56524865527-530
- ID: 14469
Cite item
Full Text
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
- Lemarie-Rieusset P.G. // The Naviez-Stokes Problem in the 21st Century. CRC Press / Taylor and Francis Group, 2016.
- 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.
- Звягин А. В. // Изв. вузов. Мат. 2016. № 10. С. 70-75.
- Foias C., Holm D. D., Titi E. S. // J. Dyn. Different. Equat. 2002. V. 14. N. 1. P. 1-35.
- Zvyagin V., Obukhovskii V., Zvyagin A. // JFPTA. 2014. V. 16. P. 27-82.
- Zvyagin V. G., Turbin M. V. // JOTA. 2011. V. 148. P. 146-163.
- Фурсиков А. В. Оптимальное управление распределёнными системами. Новосибирск: Научн. кн., 1999.
- Звягин В. Г., Турбин М. В. Математические вопросы гидродинамики вязкоупругих сред. М.: КРАСАНД УРСС, 2012.
- Zvyagin V. G. // J. Math. Sci. 2014. V. 201. P. 830-858.
- Звягин А. В. // ДАН. 2016. Т. 468. № 3. С. 251-253.
- Звягин А. В. // Диференц. уравнения. 2013. Т. 49. № 2. С. 245-249.
- Звягин А В. // Сиб. мат. журн. 2013. Т. 54. № 4. С. 807-825.
Supplementary files
