Resolvent Estimates in L p for the Stokes Operator in Lipschitz Domains

Zhongwei Shen

doi:10.1007/s00205-012-0506-7

Resolvent Estimates in L ^p for the Stokes Operator in Lipschitz Domains

Zhongwei Shen

Mathematics

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

We establish the L ^p resolvent estimates for the Stokes operator in Lipschitz domains in ℝ ^d, d ≥ 3 for {pipe}1/p-1/2{pipe} < 1/2d + εThe result implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in L ^p for (3/2) - ε < p < 3 + ε. This gives an affirmative answer to a conjecture of M. Taylor (Progr. Nonlinear Differential Equations Appl., vol. 42, pp. 320-334).

Original language	English
Pages (from-to)	395-424
Number of pages	30
Journal	Archive for Rational Mechanics and Analysis
Volume	205
Issue number	2
DOIs	https://doi.org/10.1007/s00205-012-0506-7
State	Published - Aug 2012

Bibliographical note

Funding Information:
Supported in part by NSF grant DMS-0855294.

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

Access to Document

10.1007/s00205-012-0506-7

Cite this

@article{d102c6c3680a40eda3a47518f1ee10d3,

title = "Resolvent Estimates in L p for the Stokes Operator in Lipschitz Domains",

abstract = "We establish the L p resolvent estimates for the Stokes operator in Lipschitz domains in ℝ d, d ≥ 3 for {pipe}1/p-1/2{pipe} < 1/2d + εThe result implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in L p for (3/2) - ε < p < 3 + ε. This gives an affirmative answer to a conjecture of M. Taylor (Progr. Nonlinear Differential Equations Appl., vol. 42, pp. 320-334).",

author = "Zhongwei Shen",

note = "Funding Information: Supported in part by NSF grant DMS-0855294.",

year = "2012",

month = aug,

doi = "10.1007/s00205-012-0506-7",

language = "English",

volume = "205",

pages = "395--424",

number = "2",

}

TY - JOUR

T1 - Resolvent Estimates in L p for the Stokes Operator in Lipschitz Domains

AU - Shen, Zhongwei

N1 - Funding Information: Supported in part by NSF grant DMS-0855294.

PY - 2012/8

Y1 - 2012/8

N2 - We establish the L p resolvent estimates for the Stokes operator in Lipschitz domains in ℝ d, d ≥ 3 for {pipe}1/p-1/2{pipe} < 1/2d + εThe result implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in L p for (3/2) - ε < p < 3 + ε. This gives an affirmative answer to a conjecture of M. Taylor (Progr. Nonlinear Differential Equations Appl., vol. 42, pp. 320-334).

AB - We establish the L p resolvent estimates for the Stokes operator in Lipschitz domains in ℝ d, d ≥ 3 for {pipe}1/p-1/2{pipe} < 1/2d + εThe result implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in L p for (3/2) - ε < p < 3 + ε. This gives an affirmative answer to a conjecture of M. Taylor (Progr. Nonlinear Differential Equations Appl., vol. 42, pp. 320-334).

UR - http://www.scopus.com/inward/record.url?scp=84864349372&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864349372&partnerID=8YFLogxK

U2 - 10.1007/s00205-012-0506-7

DO - 10.1007/s00205-012-0506-7

M3 - Article

AN - SCOPUS:84864349372

SN - 0003-9527

VL - 205

SP - 395

EP - 424

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 2

ER -