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

Producción científica: Article › revisión exhaustiva

43 Citas (Scopus)

Resumen

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).

Idioma original	English
Páginas (desde-hasta)	395-424
Número de páginas	30
Publicación	Archive for Rational Mechanics and Analysis
Volumen	205
N.º	2
DOI	https://doi.org/10.1007/s00205-012-0506-7
Estado	Published - ago 2012

Nota bibliográfica

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

Financiación

Supported in part by NSF grant DMS-0855294.

Financiadores	Número del financiador
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	DMS-0855294

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

Acceder al documento

10.1007/s00205-012-0506-7

Otros archivos y enlaces

Citar esto

@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 - https://www.scopus.com/pages/publications/84864349372

UR - https://www.scopus.com/pages/publications/84864349372#tab=citedBy

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 -