An introduction to the mathematical theory of the Navier-Stokes equations: 1 Linearised steady problems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1998
|
| Ausgabe: | Rev. ed., corr. 2. printing |
| Schriftenreihe: | Springer tracts in natural philosophy
38 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 463 S. |
| ISBN: | 038794172X 354094172X |
Internformat
MARC
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| 100 | 1 | |a Galdi, Giovanni P. |d 1947- |e Verfasser |0 (DE-588)11089152X |4 aut | |
| 245 | 1 | 0 | |a An introduction to the mathematical theory of the Navier-Stokes equations |n 1 |p Linearised steady problems |c Giovanni P. Galdi |
| 250 | |a Rev. ed., corr. 2. printing | ||
| 264 | 1 | |a New York u.a. |b Springer |c 1998 | |
| 300 | |a XIII, 463 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Springer tracts in natural philosophy |v 38 | |
| 490 | 0 | |a Springer tracts in natural philosophy |v ... | |
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| 830 | 0 | |a Springer tracts in natural philosophy |v 38 |w (DE-604)BV000692404 |9 38 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008721446 | ||
Datensatz im Suchindex
| _version_ | 1804127495699562496 |
|---|---|
| adam_text | Contents
Preface
vii
Preface to the First Revised Edition
ix
I Steady-State Solutions of the Navier-Stofces Equations:
Statement of the Problem and Open Questions
1
Introduction
.............................. 1
1.1
Flow in Bounded Regions
................... 4
1.2
Flow in Exterior Regions
.................... 7
1.2.1
Three-Dimensional Flow
................ 7
1.2.2
Plane Flow
....................... 9
1.3
Flow in Regions with Unbounded Boundaries
........ 12
II Basic Function Spaces and Related Inequalities
17
Introduction
.............................. 17
Basic Notations and Preliminaries
................. 18
11.1 The
Łebesgue
Spaces
Iß.................... 22
11.2 The Sobolev Spaces W™-« and Embedding Inequalities
... 27
11.3 Boundary Inequalities and the Trace of Functions of Wm q
39
11.4 Further Inequauties and Compactness Criteria in Wm·4
. . 49
IL5 The Homogeneous Sobolev Spaces DmM and
Embedding Inequalities
.................... 57
II.6 Approximation of Functions from D™1 by Smooth
Functions of Bounded Support. The Spaces Do1 *
..... 70
xii
Contents
11.7
Pointwise behavior at Large Distances of Functions
from D1
............................ 78
11.8 Boundary Trace of Rinctions from
Z?m 9(IRţ)
........ 85
11.9 Some Integral Transforms and Related Inequalities
..... 89
11.10
Notes for the Chapter
..................... 97
III The Function Spaces of Hydrodynamics
100
Introduction
.............................. 100
111.1
The Helmholtz-Weyl Decomposition of the Space L
. . . . 102
Ш.2
Relevant Properties of the Spaces Hq and Gq
........ 116
III.3 The Problem V
·
v
= ƒ..................... 120
Ш.4
The Spaces H
......................... 145
111.4.1 Bounded Domains
................... 148
111.4.2 Exterior Domains
.................... 149
111.4.3 Domains with Noncompact Boundary
........ 151
III.5 The Spaces T>Y
........................ 166
Ш.6
Approximation Problems in Spaces
Щ
and
I>¿ 9
...... 171
III.7 Notes for the Chapter
..................... 179
IV Steady Stokes Flow in Bounded Domains
182
Introduction
.............................. 182
IV.
1
Generalised Solutions. Existence and Uniqueness
...... 184
IV.2 Existence, Uniqueness, and /^-Estimates in the
Whole Space. The Stokes Fundamental Solution
....... 189
IV.3 Existence, Uniqueness, and ¿^-Estimates in a
Half-Space. Evaluation of Green s Tensor
.......... 198
IV.4 Interior ¿«-Estimates
...................... 213
IV.5 i -Estimates Near the Boundary
............... 219
IV.6 Existence, Uniqueness, and ¿^-Estimates in a Bounded
Domain. The Green s Tensor
................. 227
IV.7 Existence and Uniqueness in Holder Spaces.
Schauder
Estimates
....................... 234
IV.8 Green s Identity and Representation Formulas
........ 235
IV.9 Notes for the Chapter
..................... 240
V Steady Stokes Flow in Exterior Domains
244
Introduction
.............................. 244
V.I Generalised Solutions. Preliminary Considerations and
Regularity Properties
...................... 248
V.2 Existence and Uniqueness of Generalised Solutions for
Three-Dimensional Flow
.................... 251
V.3 Representation of Solutions. Behaviour at
Large Distances and Related Results
............. 254
V.4 Existence, Uniqueness, and ¿ -Estimates: Strong Solutions
263
Contente
xiii
V.5
Existence,
Uniqueness, and ¿«-Estimates:
^-generalised Solutions
.....................280
V.6 A Characterisation of Certain Flows with Nonzero
Boundary Data. Another Form of the Stokes Paradox
... 291
V.7 Further Existence and Uniqueness Results for
^-generalised Solutions
.....................293
V.8 Notes for the Chapter
.....................302
VI Steady Stokes Flow in Domains with
Unbounded Boundaries
304
Introduction
.............................. 304
VI.
1
Leray s Problem: Existence, Uniqueness, and Regularity
. . 309
VI.2 Decay Estimates for Flow in a Semi-infinite
Straight Channel
........................ 319
VI.3 Flow in Unbounded Channels with Unbounded Cross
Sections. Existence, Uniqueness, and Regularity
....... 327
VI.4 Pointwise Decay of Flows in Channels with Unbounded
Cross Section
.......................... 332
VI.5 Existence, Uniqueness, and Asymptotic Behaviour
of Flow Through an Aperture
................. 346
VI.6 Notes for the Chapter
..................... 354
VII
Steady
Oseen
Flow in Exterior Domains
356
Introduction
..............................356
VILI
Generalised Solutions. Regularity and Uniqueness
.....359
VII.2 Existence of Generalised Solutions for
Three-Dimensional Flow
...................362
VII.3 The
Oseen
Fundamental Solution and the
Associated Volume Potentials
................367
VII.4 Existence, Uniqueness, and
L -Estimates
in the
Whole Space
..........................382
VII.5 Existence of Generalised Solutions for Plane Flows in
Exterior Domains
.......................397
VII.6 Representation of Solutions. Behaviour at
Large Distances and Related Results
............405
VII.7 Existence, Uniqueness, and L -Estimates in
Exterior Domains
.......................413
VII.8 Limit of Vanishing Reynolds Number. Transition to
the Stokes Problem
.......·..............424
VII.9 Notes for the Chapter
.....................429
Bibliography
431
Index
467
|
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| id | DE-604.BV012820706 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:34:16Z |
| institution | BVB |
| isbn | 038794172X 354094172X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008721446 |
| oclc_num | 633915012 |
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| owner_facet | DE-703 DE-29T DE-20 DE-384 DE-355 DE-BY-UBR DE-634 |
| physical | XIII, 463 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series | Springer tracts in natural philosophy |
| series2 | Springer tracts in natural philosophy |
| spelling | Galdi, Giovanni P. 1947- Verfasser (DE-588)11089152X aut An introduction to the mathematical theory of the Navier-Stokes equations 1 Linearised steady problems Giovanni P. Galdi Rev. ed., corr. 2. printing New York u.a. Springer 1998 XIII, 463 S. txt rdacontent n rdamedia nc rdacarrier Springer tracts in natural philosophy 38 Springer tracts in natural philosophy ... (DE-604)BV009710283 1 Springer tracts in natural philosophy 38 (DE-604)BV000692404 38 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008721446&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Galdi, Giovanni P. 1947- An introduction to the mathematical theory of the Navier-Stokes equations Springer tracts in natural philosophy |
| title | An introduction to the mathematical theory of the Navier-Stokes equations |
| title_auth | An introduction to the mathematical theory of the Navier-Stokes equations |
| title_exact_search | An introduction to the mathematical theory of the Navier-Stokes equations |
| title_full | An introduction to the mathematical theory of the Navier-Stokes equations 1 Linearised steady problems Giovanni P. Galdi |
| title_fullStr | An introduction to the mathematical theory of the Navier-Stokes equations 1 Linearised steady problems Giovanni P. Galdi |
| title_full_unstemmed | An introduction to the mathematical theory of the Navier-Stokes equations 1 Linearised steady problems Giovanni P. Galdi |
| title_short | An introduction to the mathematical theory of the Navier-Stokes equations |
| title_sort | an introduction to the mathematical theory of the navier stokes equations linearised steady problems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008721446&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009710283 (DE-604)BV000692404 |
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