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The primitive equations in the scaling-invariant space L∞(L1)

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
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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