An introduction to the mathematical theory of the Navier-Stokes equations: steady-state problems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
2011
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Früher in 2 Bd. ersch. - Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIV, 1018 S. |
| ISBN: | 9780387096193 9781493950171 |
Internformat
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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 |b steady-state problems |c G. P. Galdi |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2011 | |
| 300 | |a XIV, 1018 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer monographs in mathematics | |
| 500 | |a Früher in 2 Bd. ersch. - Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 0 | 7 | |a Navier-Stokes-Gleichung |0 (DE-588)4041456-5 |2 gnd |9 rswk-swf |
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| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024565530&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-024565530 | |
Datensatz im Suchindex
| _version_ | 1810082134847651840 |
|---|---|
| adam_text |
Contents
Steady-State Solutions of the Navier-Stolces Equations:
Statement of the Problem and Open Questions
. 1
Introduction
.
I
1.1 Flow in Bounded Regions
. 4
1.2
Flow in Exterior Regions
.
H
1.2.1
Thrci^DiiiH'n.sioiiAl Flow
. 10
1.2.2
Plane Flow
. N
1.3
Flow in Region» with Unbounded Boundaries
. 17
Introduction
. 25
IM Preliminarie«
. 25
II Basic Function Spaces and Related Inequalities
. 25
?5
>5
H.I.I Bmiic Notation
. 20
II.
1.2 Danach
Sparee
and their Relevant Properties.
. 29
II
1.3
Spaces of Smooth Functions
. 35
11.1.4
Classes of Domains and their Properties
. 36
11.2
The Lebesgue Spaces I4
. 40
П.З
The Sobolev Spaces
И"*·*
and Embedding Inequalities
. 48
II.4 Boundary Inequalities and the Trace of Functions of Wm«
61
П.5
Further Inequalities and Compactness Criteria In Wm*
. 69
11.6 The Homofeneous Sobolev Spaces
&**
and Embedding
Inequalities
. 80
11.7 Approximation of Function* from
&**
by Smooth
Functions and Characterization of Space EC*
.102
11.8 The Normed Dual of
Ο£*(Ω).
The
Ѕрлст
D;m<>
.109
11.
9 Pointwim·
behavior at Large Distance« of Function« from
D1*
.115
11.10
Boundary trace of Functions from Dm
«{Щ)
.121
11.11
Some Integral Transforms and Related Inequalities
.125
11.12
Notes for the Chapter
.134
χ
Contents
III The Function Spaces of Hydrodynamics
.139
Introduction
.139
III
Л
The Helmholtz-Weyl Decomposition of the Space Lq
. 141
111.
2
Relevant Properties of the Spaces Hq and Gq
.155
111.3 The Problem V
·
ν
= ƒ
.
161
Ш.4
The Spaces
Щ
.193
111.
4.1
Bounded Domains
.196
111.4.2 Exterior Domains
.197
111.
4.3
Domains with Noncompact Boundary
.198
111.5 The Spaces V^q
.214
111.
6
Approximation Problems in Spaces H* and
Í>¿'q
.218
111.7
Notes for the Chapter
.226
IV Steady Stokes Flow in Bounded Domains
.231
Introduction
.231
IV.
1
Generalized Solutions. Existence and Uniqueness
.233
IV.
2
Existence, Uniqueness, and L9-Estimates in the
Whole Space. The Stokes Fundamental Solution
.238
IV.
3
Existence, Uniqueness, and L9-Estimates in a
Half-Space. Evaluation of Green's Tensor
.247
IV.4 Interior ¿/^-Estimates.
263
IV.5 ¿"-Estimates Near the Boundary
.271
IV.
6
Existence, Uniqueness, and L^-Estimates in a Bounded
Domain
.279
IV.
7
Existence and Uniqueness in Holder Spaces.
Schauder
Estimates
.287
IV.
8
Green's Tensor, Green's Identity and Representation
Formulas
.288
IV.9 Notes for the Chapter
.294
V Steady Stokes Flow in Exterior Domains
.299
Introduction
.299
V.I Generalized Solutions. Preliminary Considerations and
Regularity Properties
.304
V.2 Existence and Uniqueness of Generalized Solutions for
Three-Dimensional Flow
.306
V.3 Representation of Solutions. Behavior at
Large Distances and Related Results
.310
V.4 Existence, Uniqueness, and L9-Estimates: Strong
Solutions
.320
V.5 Existence, Uniqueness, and ¿^-Estimates: q-generalized
Solutions
.337
V.6 Green's Tensor and Some Related Properties
.349
V.7 A Characterization of Certain Flows with Nonzero
Boundary Data. Another Form of the Stokes Paradox
. 351
Contents xi
V.
8
Further Existence and Uniqueness Results for
qr-generalized Solutions
.354
V.9 Notes for the Chapter
.362
VI Steady Stokes Flow in Domains with Unbounded
Boundaries
.365
Introduction
.365
VI.
1
Leray's Problem: Existence, Uniqueness, and Regularity
. . 370
VI.
2
Decay Estimates for Flow in a Semi-infinite
Straight Channel
.379
VI.
3
Flow in Unbounded Channels with Unbounded Cross
Sections. Existence, Uniqueness, and Regularity
.387
VI.4 Pointwise Decay of Flows in Channels with Unbounded
Cross Section
.393
VI.
5
Existence, Uniqueness, and Asymptotic Behavior
of Flow Through an Aperture
.407
VI.6 Notes for the Chapter
.415
VII
Steady
Oseen
Flow in Exterior Domains
.417
Introduction
.417
VILI
Generalized Solutions. Regularity and Uniqueness
.420
VII.
2
Existence of Generalized Solutions for Three-Dimensional
Flow
.424
VÏI.3
The
Oseen
Fundamental Solution and the Associated
Volume Potentials
.429
VII.
4
Existence, Uniqueness, and L9-Estimates in the Whole
Space
.445
VII.
5
Existence of Generalized Solutions for Plane Flows in
Exterior Domains
.459
VII.6 Representation of Solutions. Behavior at Large Distances
and Related Results
.467
VII.
7
Existence, Uniqueness, and Lq-Estimates in Exterior
Domains
.475
VII.8 Limit of Vanishing Reynolds Number. Transition to the
Stokes Problem
.487
VII.
9
Notes for the Chapter
.492
VIII
Steady Generalized
Oseen
Flow in Exterior Domains
.495
Introduction
.495
VIII.l Generalized Solutions. Regularity and Existence
.499
VIII.2 Generalized Solutions.Uniqueness
.505
VIII.3 The Fundamental Solution to the Time-Dependent
Oseen
Problem and Related Properties
.514
VIII.4 On the Unique Solvability of the
Oseen
Initial-Value
Problem
.526
xii Contents
VIII.
5
Existence,
Uniqueness, and Pointwise Estimates of
Solutions in the Whole Space
.546
VIII.6
On the Pointwise Asymptotic Behavior of Generalized
Solutions
.554
VIII.7
Existence, Uniqueness, and I^-Estimates. The case TZ
= 0 . 560
VIII.8
Existence, Uniqueness, and ¿^-Estimates. The Case
ΤΖφΟ.
572
VIII.9 Notes for the Chapter
.578
IX Steady Navier-Stokes Flow in Bounded Domains
.583
Introduction
.583
IX.
1
Generalized Solutions. Preliminary Considerations
.586
IX.
2
On the Uniqueness of Generalized Solutions
.591
IX.
3
Existence and Uniqueness with Homogeneous Boundary
Data
.596
IX.
4
Existence and Uniqueness with Nonhomogeneous
Boundary Data
.602
IX.
5
Regularity of Generalized Solutions
.621
IX.
6
Limit of Infinite Viscosity: Transition to the Stokes
Problem
.640
IX.
7
Notes for the Chapter
.643
X Steady
Navier—
Stokes Flow in Three-Dimensional
Exterior Domains. Irrotational Case
.649
Introduction
.649
X.I Generalized Solutions. Preliminary Considerations and
Regularity Properties
.653
X.2 On the Validity of the Energy Equation for Generalized
Solutions
.659
X.3 Some Uniqueness Results
.668
X.4 Existence of Generalized Solutions
.676
X.5 On the Asymptotic Behavior of Generalized Solutions:
Preliminary Results and Representation Formulas
.688
X.6 Global Summability of Generalized Solutions
when Voo
φ
0.698
X.7 The Energy Equation and Uniqueness for Generalized
Solutions when Vqo
φ
0.705
X.8 The Asymptotic Structure of Generalized Solutions
when Vcc
φ Ο
.709
X.9 On the Asymptotic Structure of Generalized Solutions
when Uoo
= 0.721
X.10 Limit of Vanishing Reynolds Number: Transition to the
Stokes Problem
.731
X.ll Notes for the Chapter
.742
Contents xiii
XI Steady
Navier—
Stokes Flow in Three-Dimensional
Exterior Domains. Rotational Case
.745
Introduction
.745
XI.
1
Generalized Solutions. Existence of the Pressure and
Regularity Properties
.749
XI.
2
On the Energy Equation and the Uniqueness of
Generalized Solutions
.755
XI.
3
Existence of Generalized Solutions
.762
XI.4 Global Summability of Generalized Solutions when
vo
·
ω φ
0.770
XI.
5
The Energy Equation and Uniqueness for Generalized
Solutions when vo
■
ш
Φ
0.772
XI.
6
On the Asymptotic Structure of Generalized Solutions
When vo
■
ω φ
0.775
XI.
7
On the Asymptotic Structure of Generalized Solutions
When v0
·
ω
= 0.790
XI.
8
Notes for the Chapter
.795
XII
Steady
Navier—
Stokes Flow in Two-Dimensional Exterior
Domains
.797
Introduction
.797
XII.l Generalized Solutions and D-Solutions
.800
XII.2
On the Uniqueness of Generalized Solutions
.801
XII.3 On the Asymptotic Behavior of D-Solutions
.804
XII.4
Asymptotic Decay of the Vorticity and its Relevant
Consequences
.824
XII.5 Existence and Uniqueness of Solutions for Small Data
and
roo
φ
0.836
XII.6
A Necessary Condition for Non-Existence with Arbitrary
Large Data
.853
XII. 7
Global Summability of Generalized Solutions
when
ν,» φ
0.855
XII.8
The Asymptotic Structure of Generalized Solutions
when Vtx,
φΟ
.866
XII.9 Limit of Vanishing Reynolds Number: Transition to the
Stokes Problem
.885
XII.10 Notes for the Chapter
.891
XIII
Steady
Navier—
Stokes Flow in Domains with Unbounded
Boundaries
.897
Introduction
.897
XIII.l Leray's Problem: Generalized Solutions and Related
Properties
.900
XIII.2 On the Uniqueness of generalized Solutions to Leray's
Problem
.903
xiv Contents
XIII.
3
Existence
and Uniqueness of Solutions to
Leray's Problem
.910
XIII.4
Decay Estimates for Steady Flow in a Semi-Infinite
Straight Channel
.916
XIII.5
Flow in an Aperture Domain. Generalized Solutions and
Related Properties
.926
XIII.6
Energy Equation and Uniqueness for Flows in an
Aperture Domain
.930
XIII.7
Existence and Uniqueness of Flows in an
Aperture Domain
. 935
XIII.8
Global Summability of Generalized Solutions for Flow
in an Aperture Domain
.949
XIII.9
Asymptotic Structure of Generalized Solutions for Flow
in an Aperture Domain
.958
XIII.10 Notes for the Chapter
.970
Bibliography
. 975
Index
.1009
properties of boundary
problems related to the
of solutions in
as wdl as unbounded domains. Whenever the domain is
Ibis book is the
published in
1994-
In this new edition, the two volumes have been merged into one and two more
chapters on steady generalized
Oseen
flow in exterior domains and steady
Navier-
Stokes flow in three-dimensional exterior domains in presence of rotation have
been added. Most of the proofs given in the previous edition were also updated.
An introductory
Hrst
chapter describes all relevant questions treated in the book
and lists and motivates a number of significant and still open questions. It is written
in an expository style so as to be accessible also to
non
-specialists. Each chapter is
P*
used to solve them. Also» each chapter ends with a |
| any_adam_object | 1 |
| author | Galdi, Giovanni P. 1947- |
| author_GND | (DE-588)11089152X |
| author_facet | Galdi, Giovanni P. 1947- |
| author_role | aut |
| author_sort | Galdi, Giovanni P. 1947- |
| author_variant | g p g gp gpg |
| building | Verbundindex |
| bvnumber | BV039717359 |
| classification_rvk | SK 540 |
| ctrlnum | (OCoLC)767788316 (DE-599)DNB98876752X |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV039717359 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-13T12:00:42Z |
| institution | BVB |
| isbn | 9780387096193 9781493950171 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024565530 |
| oclc_num | 767788316 |
| open_access_boolean | |
| owner | DE-29T DE-188 DE-355 DE-BY-UBR DE-11 DE-20 DE-83 |
| owner_facet | DE-29T DE-188 DE-355 DE-BY-UBR DE-11 DE-20 DE-83 |
| physical | XIV, 1018 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spelling | Galdi, Giovanni P. 1947- Verfasser (DE-588)11089152X aut An introduction to the mathematical theory of the Navier-Stokes equations steady-state problems G. P. Galdi 2. ed. New York, NY [u.a.] Springer 2011 XIV, 1018 S. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Früher in 2 Bd. ersch. - Hier auch später erschienene, unveränderte Nachdrucke Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 s DE-604 Erscheint auch als Online-Ausgabe 978-0-387-09620-9 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024565530&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024565530&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Galdi, Giovanni P. 1947- An introduction to the mathematical theory of the Navier-Stokes equations steady-state problems Navier-Stokes-Gleichung (DE-588)4041456-5 gnd |
| subject_GND | (DE-588)4041456-5 |
| title | An introduction to the mathematical theory of the Navier-Stokes equations steady-state problems |
| title_auth | An introduction to the mathematical theory of the Navier-Stokes equations steady-state problems |
| title_exact_search | An introduction to the mathematical theory of the Navier-Stokes equations steady-state problems |
| title_full | An introduction to the mathematical theory of the Navier-Stokes equations steady-state problems G. P. Galdi |
| title_fullStr | An introduction to the mathematical theory of the Navier-Stokes equations steady-state problems G. P. Galdi |
| title_full_unstemmed | An introduction to the mathematical theory of the Navier-Stokes equations steady-state problems G. 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 steady state problems |
| title_sub | steady-state problems |
| topic | Navier-Stokes-Gleichung (DE-588)4041456-5 gnd |
| topic_facet | Navier-Stokes-Gleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024565530&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024565530&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT galdigiovannip anintroductiontothemathematicaltheoryofthenavierstokesequationssteadystateproblems |