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 journalArticlepeer-review

14 Citations (Scopus)


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
Issue number12
Publication statusPublished - 2016 Dec 15
Externally publishedYes


  • Global strong well-posedness
  • Primitive equations

ASJC Scopus subject areas

  • Analysis


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