The primitive equations in the scaling-invariant space L∞(L1)
- Consider the primitive equations on ◂+▸R2×(◂,▸z0,z1) with initial data a of the form a=◂+▸a1+a2, where ◂+▸a1∈◂◽.▸BUCσ(◂,▸R2;L1(◂,▸z0,z1)) and ◂+▸a2∈L ∞ σ (◂,▸R2;L1(◂,▸z0,z1)). These spaces are scaling-invariant and represent the anisotropic character of these equations. It is shown that for a1 arbitrary large and a2 sufficiently small, this set of equations admits a unique strong solution which extends to a global one and is thus strongly globally well posed for these data provided a is periodic in the horizontal variables. The approach presented depends crucially on mapping properties of the hydrostatic Stokes semigroup in the L∞(L1)-setting. It can be seen as the counterpart of the classical iteration schemes for the Navier–Stokes equations, now for the primitive equations in the L∞(L1)-setting.
Author: | Yoshikazu Giga, Mathis Gries, Matthias Hieber, Amru HusseinORCiD, Takahito Kashiwabara |
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URN: | urn:nbn:de:hbz:386-kluedo-78567 |
DOI: | https://doi.org/10.1007/s00028-021-00716-z |
ISSN: | 1424-3202 |
Parent Title (English): | Journal of Evolution Equations |
Publisher: | Springer Nature - Springer |
Document Type: | Article |
Language of publication: | English |
Date of Publication (online): | 2024/03/21 |
Year of first Publication: | 2021 |
Publishing Institution: | Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau |
Date of the Publication (Server): | 2024/03/21 |
Issue: | 21 |
Page Number: | 25 |
First Page: | 4145 |
Last Page: | 4169 |
Source: | https://link.springer.com/article/10.1007/s00028-021-00716-z |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Collections: | Open-Access-Publikationsfonds |
Licence (German): | Zweitveröffentlichung |