### Abstract

It is shown that the hydrostatic Stokes operator on Lp/σ(Ω), where Ω ⊂ ℝ^{3} is a cylindrical domain subject to mixed periodic, Dirichlet and Neumann boundary conditions, admits a bounded H^{∞}-calculus on Lp/σ(Ω) for p ∈ (1, ∞) of H^{∞}-angle 0. In particular, maximal L^{q} − L^{p}-regularity estimates for the linearized primitive equations are obtained.

Original language | English |
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Pages (from-to) | 3865-3876 |

Number of pages | 12 |

Journal | Proceedings of the American Mathematical Society |

Volume | 145 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2017 |

Externally published | Yes |

### Keywords

- H-functional calculus
- Hydrostatic Stokes operator
- Maximal L-regularity

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Bounded H<sup>∞</sup>-calculus for the hydrostatic stokes operator on L<sup>p</sup>-spaces and applications'. Together they form a unique fingerprint.

## Cite this

Giga, Y., Gries, M., Hieber, M. G., Hussein, A., & Kashiwabara, T. (2017). Bounded H

^{∞}-calculus for the hydrostatic stokes operator on L^{p}-spaces and applications.*Proceedings of the American Mathematical Society*,*145*(9), 3865-3876. https://doi.org/10.1090/proc/13676