Giga, Yoshikazu ; Gries, Mathis ; Hieber, Matthias ; Hussein, Amru ; Kashiwabara, Takahito (2024)
The primitive equations in the scaling-invariant space L∞(L1).
In: Journal of Evolution Equations, 2021, 21 (4)
doi: 10.26083/tuprints-00023424
Article, Secondary publication, Publisher's Version
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Item Type: | Article |
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Type of entry: | Secondary publication |
Title: | The primitive equations in the scaling-invariant space L∞(L1) |
Language: | English |
Date: | 3 September 2024 |
Place of Publication: | Darmstadt |
Year of primary publication: | 2021 |
Place of primary publication: | Basel |
Publisher: | Springer International Publishing |
Journal or Publication Title: | Journal of Evolution Equations |
Volume of the journal: | 21 |
Issue Number: | 4 |
DOI: | 10.26083/tuprints-00023424 |
Corresponding Links: | |
Origin: | Secondary publication DeepGreen |
Abstract: | 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. |
Uncontrolled Keywords: | Primitive equations, Rough data, Global strong well-posedness |
Status: | Publisher's Version |
URN: | urn:nbn:de:tuda-tuprints-234242 |
Classification DDC: | 500 Science and mathematics > 510 Mathematics |
Divisions: | 04 Department of Mathematics > Analysis > Angewandte Analysis |
Date Deposited: | 03 Sep 2024 13:40 |
Last Modified: | 03 Sep 2024 13:41 |
SWORD Depositor: | Deep Green |
URI: | https://tuprints.ulb.tu-darmstadt.de/id/eprint/23424 |
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