Abstract:
We continue our study of invariant forms of the classical equations of mathematical physics, such as the Maxwell equations or the Lamé system, on manifold with boundary. To this end we interpret them in terms of the de Rham complex at a certain step. On using the structure of the complex we get an insight to predict a degeneracy deeply encoded in the equations. In the present paper we develop an invariant approach to the classical Navier–Stokes equations.
The first author gratefully acknowledges the financial support of the Ministry of High Education of Iraq. The research of the second author was supported by the grant of the Russian Federation Government for scientific research under the supervision of leading scientist at the Siberian Federal University, contract no. 14.Y26.31.0006.
Received: 06.06.2018 Received in revised form: 06.09.2018 Accepted: 06.10.2018
Bibliographic databases:
Document Type:
Article
UDC:517.55
Language: English
Citation:
Azal Mera, Alexander A. Shlapunov, Nikolai Tarkhanov, “Navier–Stokes equations for elliptic complexes”, J. Sib. Fed. Univ. Math. Phys., 12:1 (2019), 3–27
This publication is cited in the following 8 articles:
A. A. Shlapunov, A. N. Polkovnikov, V. L. Mironov, “Maxwell's and Stokes's operators associated with elliptic differential complexes”, Journal of Mathematical Physics, 66:1 (2025)
Davron Aslonqulovich Juraev, Praveen Agarwal, Ali Shokri, Ebrahim E. Elsayed, Recent Trends in Fractional Calculus and Its Applications, 2024, 123
Davron Aslonqulovich Juraev, Praveen Agarwal, Ali Shokri, Ebrahim E. Elsayed, Recent Trends in Fractional Calculus and Its Applications, 2024, 147
Davron Aslonqulovich Juraev, Praveen Agarwal, Ali Shokri, Ebrahim E. Elsayed, Recent Trends in Fractional Calculus and Its Applications, 2024, 177
Ksenija V. Gagelgans, Alexander A. Shlapunov, “The Fredholm Navier–Stokes type equations for the de Rham complex over weighted Hölder spaces”, Zhurn. SFU. Ser. Matem. i fiz., 16:3 (2023), 283–299
A. Parfenov, A. Shlapunov, “On the stability phenomenon of the Navier-Stokes type equations for elliptic complexes”, Complex Var. Elliptic Equ., 66:6-7, SI (2021), 1122–1150
A. A. Shlapunov, N. Tarkhanov, “An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over ${\mathbb R}^n$”, Sib. elektron. matem. izv., 18:2 (2021), 1433–1466
Polkovnikov A., “An Open Mapping Theorem For Nonlinear Operator Equations Associated With Elliptic Complexes”, Appl. Anal., 2021
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