The Fredholm Navier--Stokes type equations for the de Rham complex over weighted H\"older spaces
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 3, pp. 283-299
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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.
@article{JSFU_2023_16_3_a0,
author = {Ksenija V. Gagelgans and Alexander A. Shlapunov},
title = {The {Fredholm} {Navier--Stokes} type equations for the de {Rham} complex over weighted {H\"older} spaces},
journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
pages = {283--299},
publisher = {mathdoc},
volume = {16},
number = {3},
year = {2023},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JSFU_2023_16_3_a0/}
}
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%0 Journal Article %A Ksenija V. Gagelgans %A Alexander A. Shlapunov %T The Fredholm Navier--Stokes type equations for the de Rham complex over weighted H\"older spaces %J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika %D 2023 %P 283-299 %V 16 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/JSFU_2023_16_3_a0/ %G en %F JSFU_2023_16_3_a0
Ksenija V. Gagelgans; Alexander A. Shlapunov. The Fredholm Navier--Stokes type equations for the de Rham complex over weighted H\"older spaces. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 3, pp. 283-299. http://geodesic.mathdoc.fr/item/JSFU_2023_16_3_a0/