### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

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

### Cite this

*Journal of Mathematical Fluid Mechanics*,

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

**Maximal L p - L q -Estimates for the stokes equation : A short proof of solonnikov's theorem.** / Geissert, Matthias; Hess, Matthias; Hieber, Matthias Georg; Schwarz, Céline; Stavrakidis, Kyriakos.

Research output: Contribution to journal › Article

*Journal of Mathematical Fluid Mechanics*, vol. 12, no. 1, pp. 47-60. https://doi.org/10.1007/s00021-008-0275-0

}

TY - JOUR

T1 - Maximal L p - L q -Estimates for the stokes equation

T2 - A short proof of solonnikov's theorem

AU - Geissert, Matthias

AU - Hess, Matthias

AU - Hieber, Matthias Georg

AU - Schwarz, Céline

AU - Stavrakidis, Kyriakos

PY - 2010/3

Y1 - 2010/3

N2 - 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

AB - 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

KW - Exterior domains

KW - Maximal L - L -estimates

KW - Stokes equation

UR - http://www.scopus.com/inward/record.url?scp=77950458637&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950458637&partnerID=8YFLogxK

U2 - 10.1007/s00021-008-0275-0

DO - 10.1007/s00021-008-0275-0

M3 - Article

AN - SCOPUS:77950458637

VL - 12

SP - 47

EP - 60

JO - Journal of Mathematical Fluid Mechanics

JF - Journal of Mathematical Fluid Mechanics

SN - 1422-6928

IS - 1

ER -