On a resolvent estimate of the Stokes system in a half space arising from a free boundary problem for the Navier-Stokes equations

Y. Shibata; S. Shimizu

doi:10.1002/mana.200710749

On a resolvent estimate of the Stokes system in a half space arising from a free boundary problem for the Navier-Stokes equations

Y. Shibata^*, S. Shimizu

^*Corresponding author for this work

School of Fundamental Science and Engineering

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

7 Citations (Scopus)

Abstract

In this paper we consider a resolvent problem of the Stokes operator with some boundary condition in the half space, which is obtained as a model problem arising in evolution free boundary problems for viscous, incompressible fiuidfiow. We show standard resolvent estimates in the L_q framework (1 <q< ∞), applying some kernel estimates to concrete solution formulas. The Volevich trick in [21] plays a fundamental role in estimating solutions.

Original language	English
Pages (from-to)	482-499
Number of pages	18
Journal	Mathematische Nachrichten
Volume	282
Issue number	3
DOIs	https://doi.org/10.1002/mana.200710749
Publication status	Published - 2009 Mar

Keywords

Free boundary problem
Gravity force
L framework
Resolvent estimate
Stokes equation
Surface tension

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1002/mana.200710749

Cite this

@article{0e64187af14e4ebc85294c8e2c59d435,

title = "On a resolvent estimate of the Stokes system in a half space arising from a free boundary problem for the Navier-Stokes equations",

abstract = "In this paper we consider a resolvent problem of the Stokes operator with some boundary condition in the half space, which is obtained as a model problem arising in evolution free boundary problems for viscous, incompressible fiuidfiow. We show standard resolvent estimates in the Lq framework (1 ",

keywords = "Free boundary problem, Gravity force, L framework, Resolvent estimate, Stokes equation, Surface tension",

author = "Y. Shibata and S. Shimizu",

year = "2009",

month = mar,

doi = "10.1002/mana.200710749",

language = "English",

volume = "282",

pages = "482--499",

journal = "Mathematische Nachrichten",

issn = "0025-584X",

publisher = "Wiley-VCH Verlag",

number = "3",

}

TY - JOUR

T1 - On a resolvent estimate of the Stokes system in a half space arising from a free boundary problem for the Navier-Stokes equations

AU - Shibata, Y.

AU - Shimizu, S.

PY - 2009/3

Y1 - 2009/3

N2 - In this paper we consider a resolvent problem of the Stokes operator with some boundary condition in the half space, which is obtained as a model problem arising in evolution free boundary problems for viscous, incompressible fiuidfiow. We show standard resolvent estimates in the Lq framework (1

AB - In this paper we consider a resolvent problem of the Stokes operator with some boundary condition in the half space, which is obtained as a model problem arising in evolution free boundary problems for viscous, incompressible fiuidfiow. We show standard resolvent estimates in the Lq framework (1

KW - Free boundary problem

KW - Gravity force

KW - L framework

KW - Resolvent estimate

KW - Stokes equation

KW - Surface tension

UR - http://www.scopus.com/inward/record.url?scp=67449128605&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67449128605&partnerID=8YFLogxK

U2 - 10.1002/mana.200710749

DO - 10.1002/mana.200710749

M3 - Article

AN - SCOPUS:67449128605

SN - 0025-584X

VL - 282

SP - 482

EP - 499

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 3

ER -

On a resolvent estimate of the Stokes system in a half space arising from a free boundary problem for the Navier-Stokes equations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this