Giga, Yoshikazu ; Gries, Mathis ; Hieber, Matthias ; Hussein, Amru ; Kashiwabara, Takahito (2021)
The primitive equations in the scalinginvariant space L∞(L1).
In: Journal of Evolution Equations, 21 (4)
doi: 10.1007/s0002802100716z
Article, Bibliographie
This is the latest version of this item.
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 scalinginvariant 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.
Item Type:  Article 

Erschienen:  2021 
Creators:  Giga, Yoshikazu ; Gries, Mathis ; Hieber, Matthias ; Hussein, Amru ; Kashiwabara, Takahito 
Type of entry:  Bibliographie 
Title:  The primitive equations in the scalinginvariant space L∞(L1) 
Language:  English 
Date:  2021 
Place of Publication:  Basel 
Publisher:  Springer International Publishing 
Journal or Publication Title:  Journal of Evolution Equations 
Volume of the journal:  21 
Issue Number:  4 
DOI:  10.1007/s0002802100716z 
Corresponding Links:  
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 scalinginvariant 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 wellposedness 
Classification DDC:  500 Science and mathematics > 510 Mathematics 
Divisions:  04 Department of Mathematics 04 Department of Mathematics > Analysis 04 Department of Mathematics > Analysis > Angewandte Analysis 
Date Deposited:  05 Sep 2024 08:56 
Last Modified:  05 Sep 2024 08:56 
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The primitive equations in the scalinginvariant space L∞(L1). (deposited 03 Sep 2024 13:40)
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