Inverse image of precompact sets and regular solutions to the Navier-Stokes equations
- We consider the initial value problem for the Navier-Stokes equations over R-3 x [0, T] with time T > 0 in the spatially periodic setting. We prove that it induces open injective mappings A(s): B-1(s) -> B-2(s-1) where B-1(s), B-2(s-1) are elements from scales of specially constructed function spaces of Bochner-Sobolev typeparametrized with the smoothness index s is an element of N. Finally, we prove that a map Asis surjective if and only if the inverse image A(s)(- 1) (K) of any pre compact set K from the range of the map Asis bounded in the Bochner space L-s([0, T], L-r(T-3))with the Ladyzhenskaya-Prodi-Serrin numbers s, r.
| Author details: | Alexander A. Shlapunov, Nikolaj Nikolaevič TarchanovORCiDGND |
|---|---|
| DOI: | https://doi.org/10.35634/vm220208 |
| ISSN: | 1994-9197 |
| ISSN: | 2076-5959 |
| Title of parent work (English): | Vestnik Udmurtskogo Universiteta. Matematika, mechanika, kompʹjuternye nauki |
| Publisher: | Udmurtskij gosudarstvennyj universitet |
| Place of publishing: | Iževsk |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2022/05/05 |
| Publication year: | 2022 |
| Release date: | 2024/08/16 |
| Tag: | Navier-Stokes equations; regular solutions |
| Volume: | 32 |
| Issue: | 2 |
| Number of pages: | 20 |
| First page: | 278 |
| Last Page: | 297 |
| Funding institution: | Foundation for the advancement of theoretical physics and mathematics; "BASIS" |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| License (German): |  Keine öffentliche Lizenz: Unter Urheberrechtsschutz |
