### Abstract

Introducing a new localization method involving Bogovskis operator we give a short and new proof for maximal L ^{p} - L ^{q} -estimates for the solution of the Stokes equation. Moreover, it is shown that, up to constants, the Stokes operator is an {\mathcal{R}} -sectorial operator in L{p}{\sigma}(\Omega), 1 <p <\infty, of {\mathcal{R}} -angle 0, for bounded or exterior domains of Ω.

Original language | English |
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Pages (from-to) | 47-60 |

Number of pages | 14 |

Journal | Journal of Mathematical Fluid Mechanics |

Volume | 12 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2010 Mar |

Externally published | Yes |

### Keywords

- Exterior domains
- Maximal L - L -estimates
- Stokes equation

### ASJC Scopus subject areas

- Applied Mathematics
- Mathematical Physics
- Computational Mathematics
- Condensed Matter Physics

## Fingerprint Dive into the research topics of 'Maximal L p - L q -Estimates for the stokes equation: A short proof of solonnikov's theorem'. Together they form a unique fingerprint.

## Cite this

Geissert, M., Hess, M., Hieber, M. G., Schwarz, C., & Stavrakidis, K. (2010). Maximal L p - L q -Estimates for the stokes equation: A short proof of solonnikov's theorem.

*Journal of Mathematical Fluid Mechanics*,*12*(1), 47-60. https://doi.org/10.1007/s00021-008-0275-0