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 |
