An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over R-n
- We consider an initial problem for the Navier-Stokes type equations associated with the de Rham complex over R-n x[0, T], n >= 3, with a positive time T. We prove that the problem induces an open injective mappings on the scales of specially constructed function spaces of Bochner-Sobolev type. In particular, the corresponding statement on the intersection of these classes gives an open mapping theorem for smooth solutions to the Navier-Stokes equations.
Author details: | Alexander ShlapunovORCiDGND, Nikolaj Nikolaevič TarchanovORCiDGND |
---|---|
DOI: | https://doi.org/10.33048/semi.2021.18.108 |
ISSN: | 1813-3304 |
Title of parent work (English): | Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija |
Publisher: | Institut Matematiki Imeni S. L. Soboleva |
Place of publishing: | Novosibirsk |
Publication type: | Article |
Language: | English |
Date of first publication: | 2021/12/01 |
Publication year: | 2021 |
Release date: | 2023/11/21 |
Tag: | Navier-Stokes equations; de Rham complex; open mapping theorem |
Volume: | 18 |
Issue: | 2 |
Number of pages: | 34 |
First page: | 1433 |
Last Page: | 1466 |
Funding institution: | Russian Science FoundationRussian Science Foundation (RSF) [N 20-11-20117] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |