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Journal of Siberian Federal University. Mathematics & Physics, 2023, Volume 16, Issue 3, Pages 283–299 (Mi jsfu1078)  

The Fredholm Navier–Stokes type equations for the de Rham complex over weighted Hölder spaces

Ksenija V. Gagelgans, Alexander A. Shlapunov

Siberian Federal University, Krasnoyarsk, Russian Federation
References:
Abstract: We consider a family of initial problems for the Navie–Stokes type equations generated by the de Rham complex in ${\mathbb R}^n \times [0,T]$, $n\geqslant 2$, with a positive time $T$ over a scale weighted anisotropic Hölder spaces. As the weights control the order of zero at the infinity with respect to the space variables for vectors fields under the consideration, this actually leads to initial problems over a compact manifold with the singular conic point at the infinity. We prove that each problem from the family induces Fredholm open injective mappings on elements of the scales. At the step $1$ of the complex we may apply the results to the classical Navier–Stokes equations for incompressible viscous fluid.
Keywords: Navier-Stokes type equations, de Rham complex, Fredholm operator equations.
Funding agency Grant number
Foundation for the Development of Theoretical Physics and Mathematics BASIS
The investigation was supported by a grant of the Foundation for the advancement of theoretical physics and mathematics "BASIS".
Received: 10.07.2022
Received in revised form: 24.08.2022
Accepted: 09.11.2022
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: English
Citation: Ksenija V. Gagelgans, Alexander A. Shlapunov, “The Fredholm Navier–Stokes type equations for the de Rham complex over weighted Hölder spaces”, J. Sib. Fed. Univ. Math. Phys., 16:3 (2023), 283–299
Citation in format AMSBIB
\Bibitem{GagShl23}
\by Ksenija~V.~Gagelgans, Alexander~A.~Shlapunov
\paper The Fredholm Navier--Stokes type equations for the de Rham complex over weighted H\"older spaces
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2023
\vol 16
\issue 3
\pages 283--299
\mathnet{http://mi.mathnet.ru/jsfu1078}
\edn{https://elibrary.ru/AQMMZL}
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