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THE PRIMITIVE EQUATIONS IN THE SCALING INVARIANT SPACE L∞ (L1)

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Title: THE PRIMITIVE EQUATIONS IN THE SCALING INVARIANT SPACE L∞ (L1)
Authors: Giga, Yoshikazu Browse this author
Gries, Mathis Browse this author
Hieber, Matthias Browse this author
Hussein, Amru Browse this author
Kashiwabara, Takahito Browse this author
Issue Date: 25-Sep-2017
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1104
Start Page: 1
End Page: 17
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)) and where BUCσ(L1) and L∞σ (L1) denote the space of all solenoidal, bounded uniformly continuous and all solenoidal, bounded functions on R2, respectively, which take values in L1 (z0, z1). These spaces are scaling invariant and represent the anisotropic character of these equations. It is shown that, if ka2kL∞σ (L1) is sufficiently small, then this set of equations has a unique, local, mild solution. If in addition a is periodic in the horizontal variables, then this solution is a strong one and extends to a unique, global, strong solution. The primitive equations are thus strongly and globally well-posed for these data. The approach depends crucially on mapping properties of the hydrostatic Stokes semigroup in the L∞(L1)-setting and can thus be seen as the counterpart of the classical iteration schemes for the Navier-Stokes equations for the situation of the primitive equations
Type: bulletin (article)
URI: http://hdl.handle.net/2115/67186
http://eprints3.math.sci.hokudai.ac.jp/2413/
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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