article · ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE · 2019

Primitive equations with linearly growing initial data

Amru Hussein, Martin Saal, Okihiro Sawada

Cited by 1Open access

Abstract

The primitive equations in a 3D infinite layer domain are considered with linearly growing initial data in the horizontal direction, which illustrates the global atmospheric rotating or straining flows. On the boundaries, Dirichlet, Neumann or mixed boundary conditions are imposed. The Ornstein-Uhlenbeck type operator appears in the linear parts, so the semigroup theory is established by Trotter's arguments due to decomposition of infinitesimal generators. To obtain smoothing properties of the semigroup, derivatives of the associated kernel are calculated. For proving time-local existence and uniqueness of mild solutions, the adapted Fujita-Kato scheme is used in certain Sobolev spaces.

Cite this paper

APA 7

Hussein, A., Saal, M., & Sawada, O. (2019). Primitive equations with linearly growing initial data. ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 889–911. https://doi.org/10.2422/2036-2145.201701_012

MLA 9

Hussein, Amru, et al. “Primitive equations with linearly growing initial data.” ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2019, pp. 889–911, https://doi.org/10.2422/2036-2145.201701_012.

Chicago

Hussein, Amru, Martin Saal, and Okihiro Sawada. 2019. “Primitive equations with linearly growing initial data.” ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE: 889–911. https://doi.org/10.2422/2036-2145.201701_012.

Harvard

Hussein, A., Saal, M. and Sawada, O. (2019) ‘Primitive equations with linearly growing initial data’, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, pp. 889–911. Available at: https://doi.org/10.2422/2036-2145.201701_012.

BibTeX

@article{hussein2019primitive,
  title = {{Primitive equations with linearly growing initial data}},
  author = {Hussein, Amru and Saal, Martin and Sawada, Okihiro},
  journal = {ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE},
  pages = {889--911},
  year = {2019},
  doi = {10.2422/2036-2145.201701_012}
}

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