Giga, Yoshikazu ; Gries, Mathis ; Hieber, Matthias ; Hussein, Amru ; Kashiwabara, Takahito (2021)
The primitive equations in the scaling-invariant space L∞(L1).
In: Journal of Evolution Equations, 21 (4)
doi: 10.1007/s00028-021-00716-z
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 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.
| 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 scaling-invariant 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/s00028-021-00716-z |
| 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 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 |
| 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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| Suche nach Titel in: | TUfind oder in Google |
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The primitive equations in the scaling-invariant space L∞(L1). (deposited 03 Sep 2024 13:40)
- The primitive equations in the scaling-invariant space L∞(L1). (deposited 05 Sep 2024 08:56) [Currently Displayed]
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