### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

^{∞}-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

**Bounded H ^{∞}-calculus for the hydrostatic stokes operator on L^{p}-spaces and applications.** / Giga, Yoshikazu; Gries, Mathis; Hieber, Matthias Georg; Hussein, Amru; Kashiwabara, Takahito.

Research output: Contribution to journal › Article

^{∞}-calculus for the hydrostatic stokes operator on L

^{p}-spaces and applications',

*Proceedings of the American Mathematical Society*, vol. 145, no. 9, pp. 3865-3876. https://doi.org/10.1090/proc/13676

^{∞}-calculus for the hydrostatic stokes operator on L

^{p}-spaces and applications. Proceedings of the American Mathematical Society. 2017;145(9):3865-3876. https://doi.org/10.1090/proc/13676

}

TY - JOUR

T1 - Bounded H∞-calculus for the hydrostatic stokes operator on Lp-spaces and applications

AU - Giga, Yoshikazu

AU - Gries, Mathis

AU - Hieber, Matthias Georg

AU - Hussein, Amru

AU - Kashiwabara, Takahito

PY - 2017

Y1 - 2017

N2 - It is shown that the hydrostatic Stokes operator on Lp/σ(Ω), where Ω ⊂ ℝ3 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 Lq − Lp-regularity estimates for the linearized primitive equations are obtained.

AB - It is shown that the hydrostatic Stokes operator on Lp/σ(Ω), where Ω ⊂ ℝ3 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 Lq − Lp-regularity estimates for the linearized primitive equations are obtained.

KW - H-functional calculus

KW - Hydrostatic Stokes operator

KW - Maximal L-regularity

UR - http://www.scopus.com/inward/record.url?scp=85021426982&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021426982&partnerID=8YFLogxK

U2 - 10.1090/proc/13676

DO - 10.1090/proc/13676

M3 - Article

AN - SCOPUS:85021426982

VL - 145

SP - 3865

EP - 3876

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 9

ER -