The formation of shocks in 3-dimensional fluids:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Zürich
European Math. Society
2007
|
| Series: | EMS monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltstext Ausfuehrliche Beschreibung Inhaltsverzeichnis |
| Physical Description: | VIII, 992 S. |
| ISBN: | 9783037190319 3037190310 |
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MARC
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| 100 | 1 | |a Christodulu, Dēmētrēs Ch. |d 1951- |e Verfasser |0 (DE-588)1049266897 |4 aut | |
| 245 | 1 | 0 | |a The formation of shocks in 3-dimensional fluids |c Demetrios Christodoulou |
| 264 | 1 | |a Zürich |b European Math. Society |c 2007 | |
| 300 | |a VIII, 992 S. | ||
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Record in the Search Index
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|---|---|
| adam_text |
Contents
Prologue
and Summary
. 1
1
Relativistic Fluids and Nonlinear Wave Equations.
The Equations of Variation
. 23
2
The Basic Geometric Construction
. 39
3
The Acoustical Structure Equations
. 53
4
The Acoustical Curvature
. 85
5
The Fundamental Energy Estimate
. 99
6
Construction of the Commutation Vectorfields
. 139
7
Outline of the Derived Estimates of Each Order
. 169
8
Régularisation
of the Propagation Equation for
ţftr/
.
Estimates for the Top Order Angular Derivatives of
χ
. 203
9
Regularization of the Propagation Equation for
φ.μ.
Estimates for the Top Order Spatial Derivatives of
μ
. 275
10
Control of the Angular Derivatives of the First Derivatives of the x'
.
Assumptions and Estimates in Regard to
χ
. 329
Part
1 :
Control of the angular derivatives
of the first derivatives of the x'
. 329
Part
2:
Bounds for the quantities
(íl-ř/)6/
and ('i
···'/)
ą
. 403
11
Control of the Spatial Derivatives of the First Derivatives of the x'
.
Assumptions and Estimates in Regard to
μ
. 473
Part
1 :
Control of the spatial derivatives of the
first derivatives of the x'
. 473
Part
2:
Bounds for the quantities ih"'l) Q'm
,
and
^1"^
P'm
г
. 589
12
Recovery of the Acoustical Assumptions. Estimates for Up to the Next
to the Top Order Angular Derivatives of
χ
and Spatial Derivatives of
μ
. . . 665
viii Contents
13
The Error Estimates Involving the Top Order Spatial Derivatives of the
Acoustical Entities. The Energy Estimates. Recovery of the Bootstrap
Assumptions. Statement and Proof of the Main Theorem:
Existence up to Shock Formation
. 741
Parti: Derivation of the properties Cl, C2, C3
. 741
Part
2:
The error estimates of the acoustical entities
. 757
Part
3:
The energy estimates
. 831
Part
4:
Recovery of assumption J. Recovery of the bootstrap
assumption. Proof of the main theorem
. 874
14
Sufficient Conditions on the Initial Data for the Formation
of a Shock in the Evolution
. 893
15
The Nature of the Singular Hypersurface. The Invariant Curves.
The Trichotomy Theorem. The Structure of the Boundary of
the Domain of the Maximal Solution
. 927
Epilogue
. 977
Bibliography
. 987
Index
. 989 |
| adam_txt |
Contents
Prologue
and Summary
. 1
1
Relativistic Fluids and Nonlinear Wave Equations.
The Equations of Variation
. 23
2
The Basic Geometric Construction
. 39
3
The Acoustical Structure Equations
. 53
4
The Acoustical Curvature
. 85
5
The Fundamental Energy Estimate
. 99
6
Construction of the Commutation Vectorfields
. 139
7
Outline of the Derived Estimates of Each Order
. 169
8
Régularisation
of the Propagation Equation for
ţftr/
.
Estimates for the Top Order Angular Derivatives of
χ
. 203
9
Regularization of the Propagation Equation for
φ.μ.
Estimates for the Top Order Spatial Derivatives of
μ
. 275
10
Control of the Angular Derivatives of the First Derivatives of the x'
.
Assumptions and Estimates in Regard to
χ
. 329
Part
1 :
Control of the angular derivatives
of the first derivatives of the x'
. 329
Part
2:
Bounds for the quantities
(íl-ř/)6/
and ('i
···'/)
ą
. 403
11
Control of the Spatial Derivatives of the First Derivatives of the x'
.
Assumptions and Estimates in Regard to
μ
. 473
Part
1 :
Control of the spatial derivatives of the
first derivatives of the x'
. 473
Part
2:
Bounds for the quantities ih"'l) Q'm
,
and
^1"^
P'm
г
. 589
12
Recovery of the Acoustical Assumptions. Estimates for Up to the Next
to the Top Order Angular Derivatives of
χ
and Spatial Derivatives of
μ
. . . 665
viii Contents
13
The Error Estimates Involving the Top Order Spatial Derivatives of the
Acoustical Entities. The Energy Estimates. Recovery of the Bootstrap
Assumptions. Statement and Proof of the Main Theorem:
Existence up to Shock Formation
. 741
Parti: Derivation of the properties Cl, C2, C3
. 741
Part
2:
The error estimates of the acoustical entities
. 757
Part
3:
The energy estimates
. 831
Part
4:
Recovery of assumption J. Recovery of the bootstrap
assumption. Proof of the main theorem
. 874
14
Sufficient Conditions on the Initial Data for the Formation
of a Shock in the Evolution
. 893
15
The Nature of the Singular Hypersurface. The Invariant Curves.
The Trichotomy Theorem. The Structure of the Boundary of
the Domain of the Maximal Solution
. 927
Epilogue
. 977
Bibliography
. 987
Index
. 989 |
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| dewey-full | 532.5/ |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532.5/ |
| dewey-search | 532.5/ |
| dewey-sort | 3532.5 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| discipline_str_mv | Physik Mathematik |
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| index_date | 2024-07-02T18:52:49Z |
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| spelling | Christodulu, Dēmētrēs Ch. 1951- Verfasser (DE-588)1049266897 aut The formation of shocks in 3-dimensional fluids Demetrios Christodoulou Zürich European Math. Society 2007 VIII, 992 S. txt rdacontent n rdamedia nc rdacarrier EMS monographs in mathematics Hydrodynamics Stoßwelle (DE-588)4057760-0 gnd rswk-swf Nichtlineare Wellengleichung (DE-588)4042104-1 gnd rswk-swf Flüssigkeit (DE-588)4017621-6 gnd rswk-swf Flüssigkeit (DE-588)4017621-6 s Nichtlineare Wellengleichung (DE-588)4042104-1 s Stoßwelle (DE-588)4057760-0 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2897211&prov=M&dok_var=1&dok_ext=htm Inhaltstext text/html http://www.ems-ph.org/book.php?proj_nr=51 Ausfuehrliche Beschreibung Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016093837&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Christodulu, Dēmētrēs Ch. 1951- The formation of shocks in 3-dimensional fluids Hydrodynamics Stoßwelle (DE-588)4057760-0 gnd Nichtlineare Wellengleichung (DE-588)4042104-1 gnd Flüssigkeit (DE-588)4017621-6 gnd |
| subject_GND | (DE-588)4057760-0 (DE-588)4042104-1 (DE-588)4017621-6 |
| title | The formation of shocks in 3-dimensional fluids |
| title_auth | The formation of shocks in 3-dimensional fluids |
| title_exact_search | The formation of shocks in 3-dimensional fluids |
| title_exact_search_txtP | The formation of shocks in 3-dimensional fluids |
| title_full | The formation of shocks in 3-dimensional fluids Demetrios Christodoulou |
| title_fullStr | The formation of shocks in 3-dimensional fluids Demetrios Christodoulou |
| title_full_unstemmed | The formation of shocks in 3-dimensional fluids Demetrios Christodoulou |
| title_short | The formation of shocks in 3-dimensional fluids |
| title_sort | the formation of shocks in 3 dimensional fluids |
| topic | Hydrodynamics Stoßwelle (DE-588)4057760-0 gnd Nichtlineare Wellengleichung (DE-588)4042104-1 gnd Flüssigkeit (DE-588)4017621-6 gnd |
| topic_facet | Hydrodynamics Stoßwelle Nichtlineare Wellengleichung Flüssigkeit |
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