Global Strong Well-Posedness of the Three Dimensional Primitive Equations in Lp -Spaces

Matthias Georg Hieber, Takahito Kashiwabara

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

In this article, an Lp-approach to the primitive equations is developed. In particular, it is shown that the three dimensional primitive equations admit a unique, global strong solution for all initial data a∈[Xp,D(Ap)]1/p provided p∈ [ 6 / 5 , ∞). To this end, the hydrostatic Stokes operator Ap defined on Xp, the subspace of Lp associated with the hydrostatic Helmholtz projection, is introduced and investigated. Choosing p large, one obtains global well-posedness of the primitive equations for strong solutions for initial data a having less differentiability properties than H1, hereby generalizing in particular a result by Cao and Titi (Ann Math 166:245–267, 2007) to the case of non-smooth initial data.

Original languageEnglish
Pages (from-to)1077-1115
Number of pages39
JournalArchive for Rational Mechanics and Analysis
Volume221
Issue number3
DOIs
Publication statusPublished - 2016 Sep 1
Externally publishedYes

Fingerprint

Primitive Equations
Lp Spaces
Well-posedness
Hydrostatics
Strong Solution
Three-dimensional
Stokes Operator
Global Well-posedness
Hermann Von Helmholtz
Differentiability
Subspace
Projection

ASJC Scopus subject areas

  • Analysis
  • Mechanical Engineering
  • Mathematics (miscellaneous)

Cite this

Global Strong Well-Posedness of the Three Dimensional Primitive Equations in Lp -Spaces. / Hieber, Matthias Georg; Kashiwabara, Takahito.

In: Archive for Rational Mechanics and Analysis, Vol. 221, No. 3, 01.09.2016, p. 1077-1115.

Research output: Contribution to journalArticle

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