Global strong Lp well-posedness of the 3D primitive equations with heat and salinity diffusion

Matthias Hieber, Amru Hussein, Takahito Kashiwabara

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Consider the full primitive equations, i.e. the three dimensional primitive equations coupled to the equation for temperature and salinity, and subject to outer forces. It is shown that this set of equations is globally strongly well-posed for arbitrary large initial data lying in certain interpolation spaces, which are explicitly characterized as subspaces of H2/p,p, 1<p<∞, satisfying certain boundary conditions. In particular, global well-posedness of the full primitive equations is obtained for initial data having less differentiability properties than H1, hereby generalizing a result by Cao and Titi (2007) [5] to the case of non-smooth data. In addition, it is shown that the solutions are exponentially decaying provided the outer forces possess this property.

Original languageEnglish
Pages (from-to)6950-6981
Number of pages32
JournalJournal of Differential Equations
Volume261
Issue number12
DOIs
Publication statusPublished - 2016 Dec 15
Externally publishedYes

Fingerprint

Primitive Equations
Salinity
Well-posedness
Interpolation
Heat
Boundary conditions
Interpolation Spaces
Global Well-posedness
Differentiability
Temperature
Subspace
Three-dimensional
Arbitrary
Hot Temperature

Keywords

  • Global strong well-posedness
  • Primitive equations

ASJC Scopus subject areas

  • Analysis

Cite this

Global strong Lp well-posedness of the 3D primitive equations with heat and salinity diffusion. / Hieber, Matthias; Hussein, Amru; Kashiwabara, Takahito.

In: Journal of Differential Equations, Vol. 261, No. 12, 15.12.2016, p. 6950-6981.

Research output: Contribution to journalArticle

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