Studies in phase space analysis with applications to PDEs:
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
New York, N.Y. [u.a.]
Springer
2013
|
| Series: | Progress in nonlinear differential equations and their applications; 84
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 379 S. |
| ISBN: | 9781461463474 9781461463481 |
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MARC
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| 245 | 1 | 0 | |a Studies in phase space analysis with applications to PDEs |c Massimo Cicognani, ... eds. |
| 264 | 1 | |a New York, N.Y. [u.a.] |b Springer |c 2013 | |
| 300 | |a XVII, 379 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Progress in nonlinear differential equations and their applications; 84 | |
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| 700 | 1 | |a Cicognani, Massimo |e Sonstige |4 oth | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-026144178 | ||
Record in the Search Index
| _version_ | 1804150582355689472 |
|---|---|
| adam_text | Contents
1
The Water-Wave
Equations: From Zakharov to
Euler
............. 1
Thomas Alazard, Nicolas Burq, and Claude Zuily
1.1
Introduction
.............................................. 1
1.2
Low Regularity Cauchy Theory
............................. 4
1.3
From Zakharov to
Euler
.................................... 6
1.3.1
The Vanational Theory
............................. 6
1.3.2
The Main Result
.................................. 7
1.3.3
Straightening the Free Boundary
..................... 8
1.3.4
The Dirichlet-Neumann Operator
.................... 9
1.3.5
Preliminaries
..................................... 10
1.3.6
The Regularity Results
............................. 12
1.3.7
Proof of the Lemmas
............................... 13
References
..................................................... 20
2
On the Characterization of Pseudodifferential Operators
(Old and New)
.............................................. 21
Jean-Michel Bony
2.1
Introduction
.............................................. 21
2.2 Weyl-Hörmander
Calculus
................................. 22
2.2.1
Admissible Metrics
................................ 23
2.2.2
Symbolic Calculus
................................ 24
2.2.3
Can One Use Only Metrics Without Symplectic
Eccentricity?
..................................... 25
2.3
Characterization of Pseudodifferential Operators
............... 26
2-3.1
Geodesic Temperance
.............................. 26
2.3.2
Characterization
................................... 27
2.3.3
Functional Calculus
............................... 29
2.4
Sufficient Conditions for the Geodesic Temperance
............. 30
2.4.1
Proof of Theorem
2.5
(i)
............................ 31
2.4.2
Proof of Theorem
2.5
(ii)
........................... 33
References
..................................................... 34
Contents
Improved
Multipolar
Hardy Inequalities
........................ 35
Cristian Cazacu and
Enrique Zuazua
3.1
Introduction..............................................
36
3.2
Preliminaries: Some Strategies to Prove Hardy-Type
Inequalities
.............................................. 39
3.3
Multipolar
Hardy Inequalities
............................... 40
3.4
New Bounds for the Bipolar Hardy Inequality
in Bounded Domains
...................................... 46
3.5
Further Comments and Open Problems
....................... 50
References
..................................................... 51
The Role of Spectral Anisotropy in the Resolution of the
Three-Dimensional Navier-Stokes Equations
.................... 53
lean-Yves
Chemin, Isabelle
Gallagher, and
Chloé
Mullaert
4.1
Introduction
.............................................. 53
4.2
Preliminaries: Notation and
Anisotropie
Function Spaces
........ 57
4.3
Proof of Theorem
4.3...................................... 59
4.3.1
Decomposition of the Initial Data
.................... 59
4.3.2
Construction of an Approximate Solution and End
of the Proof of Theorem
4.3......................... 60
4.3.3
Proof of the Estimates on the Approximate
Solution (Lemma
4.1).............................. 61
4.3.4
Proof of the Estimates on the Remainder
(Lemma
4.2) ..................................... 62
4.4
Estimates on the Linear Transport-Diffusion Equation
........... 68
References
..................................................... 79
Schrödmger
Equations in Modulation Spaces
.................... 81
Elena
Cordero,
Fabio Nicola,
and
Luigi Rodino
5.1
Introduction
.............................................. 81
5.2
Modulation Spaces and Time-Frequency Analysis
.............. 84
5.2.1
Modulation Spaces
................................ 85
5.2.2 Gabor
Frames
[23] ................................ 88
5.3
Classical Fourier Integral Operators in Rrf
..................... 89
5.4
Boundedness of FIOs on Modulation Spaces and Wiener
Amalgam Spaces
......................................... 91
5.5
Other Results
............................................. 96
References
..................................................... 97
New Maximal Regularity Results for the Heat Equation
in Exterior Domains, and Applications
.......................... 101
Raphaël Danchin
and
Piotr Bogusław
Mucha
6.1
Introduction
.............................................. 101
6.2
Tools
..................................................... 104
6.2.1
Besov
Spaces on the Whole Space
................... 104
6.2.2
Besov
Spaces on Domains
.......................... 106
Contents xi
6.3
A Priori Estimates for the Heat Equation
......................108
6.3.1
The Heat Equation
m
the Half-Space
.................109
6.3.2
The Exterior Domain Case
..........................110
6.3.3
The Bounded
Domam
Case
.........................121
6.4
Applications
.............................................122
References
.....................................................127
7
Cauchy Problem for Some
2x2
Hyperbolic Systems
of Pseudo-differential Equations with Nondiagonalisable
Principal Part
.............................................. 129
Todor Gramchev and Michael Ruzhansky
7.1
Introduction
..............................................129
7.2
Reduction and
Well-Posedness in Anisotropie Sobolev
Spaces
.... 131
7.3
Cauchy Problem for
2x2
Hyperbolic Pseudo-differential
Systems
.................................................133
7.4
Final Remarks
............................................143
References
.....................................................144
8
Scattering Problem for Quadratic Nonlinear Klein-Gordon
Equation in 2D
............................................. 147
Nakao Hayashi and Pavel I. Naumkin
8.1
Introduction
..............................................147
8.2
Preliminary Estimates
.....................................151
8.3
Proof of Theorem
8.1......................................151
8.4
Proof of Theorem
8.2......................................155
References
.....................................................158
9
Global Solutions to the
3-D
Incompressible bihomogeneous
Navier-Stokes System with Rough Density
...................... 159
Jingchi Huang, Marius Paicu, and Ping Zhang
9.1
Introduction
..............................................160
9.2
The Estimate of the Transport Equation
.......................165
9 3
The Estimate of the Pressure
................................167
9.4
The Proof of Theorem
9.3..................................173
9.4.1
The Estimate of uh
................................ 173
9.4.2
The Estimate of u3
................................ 176
9.4.3
The Proof of Theorem
9.3.......................... 177
References
..................................................... 179
10
The Cauchy Problem for the Euler-Poisson System and
Derivation of the Zakharov-Kuznetsov Equation
................. 181
David Lannes, Felipe Linares, and
Jean-Claude Saut
10.1
Introduction
..............................................182
10.1.1 General Setting
...................................182
10.1.2
Organization of the Paper
...........................185
10.1.3
Notations
........................................185
xii Contents
10.2
The Cauchy Problem for the Euler-Poisson System
.............186
10.2.1
Solving the Elliptic Part
............................186
10.2.2
Local Well-Posedness
..............................190
10.3
The Long-Wave Limit of the Euler-Poisson System
............191
10.3.1
The Cauchy Problem Revisited
......................192
10.3.2
The ZK Approximation to the Euler-Poisson System
.... 197
10.3.3
Justification of the Zakharov-Kuznetsov
Approximation
....................................202
10.4
The Euler-Poisson System with Isothermal Pressure
............205
10.4.1
The Cauchy Problem for the
Euler—Poisson
System
with Isothermal Pressure
...........................205
10.4.2
Derivation of a Zakharov-Kuznetsov Equation
in Presence of Isothermal Pressure
...................208
10.4.3
Justification of the Zakharov-Kuznetsov
Approximation
....................................211
References
.....................................................212
11
L1 Estimates for Oscillating Integrals Related to Structural
Damped Wave Models
.......................................215
Takashi Narazaki and Michael Reissig
11.1
Introduction
..............................................215
11.2
If Estimates for a Model Oscillating Integrals
.................218
11.3
The General Case
σ
=
...................................224
11.4
The Case
σ
є
(0,1/2) .....................................226
11.4.1
L1
Estimates for Small Frequencies
..................226
11.4.2
L1 Estimates for Large Frequencies
..................234
11.4.3
L°° Estimates
.....................................240
11.4.4
If
—Iß
Estimates not Necessarily
on the Conjugate Line
..............................241
11.5
The Case
σ
e
(1/2,1).....................................242
11.5.1
L1
Estimates for Small Frequencies
..................242
11.5.2
L1 Estimates for Large Frequencies
..................247
11.5.3
IT Estimates
.....................................253
11.5.4
If
—Iß
Estimates not Necessarily
on the Conjugate Line
..............................253
Appendix
.......................................................255
References
.....................................................258
12
On the Cauchy Problem for Noneffectively Hyperbolic
Operators, a Transition Case
..................................259
Tatsuo Nishitani
12.1
Introduction
..............................................259
12.2
Case
СПТЅ
= {0}........................................263
12.2.1
A Priori Estimates
..................................268
12.3
Case
СПТЅ
^
{0}........................................283
12.3.1
Elementary Decomposition
.........................285
Contents
хні
12.3.2
A Priori Estimates
.................................286
12.3.3
Geometric Observations
............................287
References
.....................................................290
13
A Note on Unique Continuation for Parabolic Operators
with Singular Potentials
......................................291
Takashi Okaji
13.1
Introduction
..............................................291
13.2
Main Results
.............................................295
13.3
Sufficient Conditions for {Q a
.............................298
13.4
Outline of Proof of Theorem
13.3............................300
13.5
Outline of Proof of Theorem
13.4............................304
13.6
Outline of Proofs of Theorems
13.5
and
13.6..................309
Appendix
......................................................310
References
.....................................................311
14
On the Problem of
Positivity
of Pseudodifferential Systems
........313
Alberto
Panneggiarli
14.1
Introduction
..............................................313
14.2
Background on the
Weyl-Hörmander
Calculus
.................314
14.3
The Basic
Positivity
Estimates in the Scalar Case
...............317
14.3.1
The Case of Classical (Second-Order) ydos
...........319
14.4
The
Sharp-Gårding
and the Fefferman-Phong Inequality
for Systems
..............................................320
14.5
The Approximate Positive and Negative Parts
of a First-Order System
....................................327
References
.....................................................334
15
Scattering Problems for Symmetric Systems with Dissipative
Boundary Conditions
........................................337
Vesselm Petkov
15.1
Introduction
..............................................337
15.2
Wave Operators
...........................................339
15.3
Asymptotically Disappearing Solutions for Maxwell System
.....343
15.4
Representation of the Scattering Kernel
.......................346
15.5
Back Scattering Inverse Problem for the Scattering Kernel
.......348
References
.....................................................353
16
Kato
Smoothing Effect for
Schrödinger
Operator
................355
Luc Robbiano
16.1
Introduction
..............................................355
16.2
Results Global in Time
.....................................356
16.3
Results Local in Time in
W
................................358
16.4
Results in Exterior Domains
................................361
16.4.1
Geometrical Control Condition
......................361
16-4.2
Damping Condition
................................362
xiv Contents
16.5
Related Problems
.........................................364
16.5.1
Analytic and
С
Smoothing Effect
...................364
16.5.2
Strichartz Estimates and Dispersive Estimates
..........366
References
.....................................................366
17
On the Cauchy Problem for NLS with Randomized Initial Data
371
Nicola Visciglia
17.1
Introduction
..............................................371
17.2
Probabilistic A-Prion Estimates
..............................374
17.3
Proof of Theorem
17.1 ....................................374
17.4
Deterministic Theory via Inhomogeneous Strichartz
Estimates for L2 Supercritical NLS
...........................374
17.5
Proof of Theorem
17.2.....................................379
References
.....................................................379
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| id | DE-604.BV041168939 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:41:13Z |
| institution | BVB |
| isbn | 9781461463474 9781461463481 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026144178 |
| oclc_num | 843057491 |
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| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XVII, 379 S. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series2 | Progress in nonlinear differential equations and their applications; 84 |
| spelling | Studies in phase space analysis with applications to PDEs Massimo Cicognani, ... eds. New York, N.Y. [u.a.] Springer 2013 XVII, 379 S. txt rdacontent n rdamedia nc rdacarrier Progress in nonlinear differential equations and their applications; 84 Phasenraum (DE-588)4139912-2 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Phasenraum (DE-588)4139912-2 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Cicognani, Massimo Sonstige oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026144178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Studies in phase space analysis with applications to PDEs Phasenraum (DE-588)4139912-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4139912-2 (DE-588)4044779-0 |
| title | Studies in phase space analysis with applications to PDEs |
| title_auth | Studies in phase space analysis with applications to PDEs |
| title_exact_search | Studies in phase space analysis with applications to PDEs |
| title_full | Studies in phase space analysis with applications to PDEs Massimo Cicognani, ... eds. |
| title_fullStr | Studies in phase space analysis with applications to PDEs Massimo Cicognani, ... eds. |
| title_full_unstemmed | Studies in phase space analysis with applications to PDEs Massimo Cicognani, ... eds. |
| title_short | Studies in phase space analysis with applications to PDEs |
| title_sort | studies in phase space analysis with applications to pdes |
| topic | Phasenraum (DE-588)4139912-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Phasenraum Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026144178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT cicognanimassimo studiesinphasespaceanalysiswithapplicationstopdes |