Hydrodynamic limits of the Boltzmann equation:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Series: | Lecture notes in mathematics
1971 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 181 - 186 |
| Physical Description: | XII, 188 S. graph. Darst. 24 cm |
| ISBN: | 9783540928461 9783540928478 |
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MARC
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Record in the Search Index
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| adam_text | CONTENTS INTRODUCTION 1 1.1 THE SIXTH PROBLEM OF HUBERT 1 1.1.1 THE
MATHEMATICAL TREATMENT OF THE AXIOMS OF PHYSICS 1 1.1.2 FROM MICROSCOPIC
TO MACROSCOPIC EQUATIONS 2 1.2 FORMAL STUDY OF THE TRANSITIONS 2 1.2.1
SCALINGS 3 1.2.2 HYDRODYNAMIC LIMITS 3 1.3 THE PROBABILISTIC APPROACH 5
1.3.1 THE EULER LIMIT 6 1.3.2 THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS
7 1.4 THE ANALYTIC APPROACH 8 1.4.1 FORMAL DERIVATIONS 8 1.4.2
CONVERGENCE PROOFS BASED ON ASYMPTOTIC EXPANSIONS.. 9 1.4.3 CONVERGENCE
PROOFS BASED ON SPECTRAL RESULTS 10 1.4.4 A PROGRAM OF DERIVING WEAK
SOLUTIONS 10 THE BOLTZMANN EQUATION AND ITS FORMAL HYDRODYNAMIC LIMITS
13 2.1 FORMULATION AND FUNDAMENTAL PROPERTIES OF THE BOLTZMANN EQUATION
15 2.1.1 THE BOLTZMANN COLLISION INTEGRAL 15 2.1.2 LOCAL CONSERVATION
LAWS 19 2.1.3 BOLTZMANN S H THEOREM 21 2.2 ORDERS OF MAGNITUDE AND
QUALITATIVE BEHAVIOUR OF THE BOLTZMANN EQUATION 22 2.2.1 NONDIMENSIONAL
FORM OF THE BOLTZMANN EQUATION 22 2.2.2 HYDRODYNAMIC REGIMES 24 2.2.3
CORRECTIONS TO HYDRODYNAMIC APPROXIMATIONS 27 2.2.4 TAKING INTO ACCOUNT
THE BOUNDARY 29 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/991529499
DIGITALISIERT DURCH CONTENTS 2.3 MATHEMATICAL THEORIES FOR THE BOLTZMANN
EQUATION 30 2.3.1 PERTURBATIVE FRAMEWORK : GLOBAL EXISTENCE OF SMOOTH
SOLUTIONS 30 2.3.2 PHYSICAL FRAMEWORK : GLOBAL EXISTENCE OF RENORMALIZED
SOLUTIONS 33 2.3.3 FURTHER RESULTS IN ONE SPACE DIMENSION 43
MATHEMATICAL TOOLS FOR THE DERIVATION OF HYDRODYNAMIC LIMITS 47 3.1
PHYSICAL A PRIORI ESTIMATES : DEFINITION OF SUITABLE FUNCTIONAL SPACES
47 3.1.1 THE ENTROPY BOUND 48 3.1.2 THE DARROZES-GUIRAUD INFORMATION 53
3.1.3 THE ENTROPY DISSIPATION BOUND 54 3.2 PROPERTIES OF THE COLLISION
OPERATOR : RELAXATION TOWARDS EQUILIBRIUM AND REGULARIZATION IN V
VARIABLES 56 3.2.1 SOME RESULTS IN THE NON PERTURBATIVE FRAMEWORK 56
3.2.2 COERCIVITY OF THE LINEARIZED COLLISION OPERATOR 58 3.2.3 IMPROVING
INTEGRABILITY WITH RESPECT TO THE V VARIABLES 64 3.3 PROPERTIES OF THE
FREE TRANSPORT OPERATOR : DISPERSION AND AVERAGING LEMMAS 66 3.3.1 L 2
AVERAGING LEMMAS 67 3.3.2 DISPERSIVE PROPERTIES OF THE FREE-TRANSPORT
OPERATOR 70 3.3.3 L 1 AVERAGING LEMMAS 72 3.3.4 THE CASE OF A SPATIAL
DOMAIN WITH BOUNDARIES 76 THE INCOMPRESSIBLE NAVIER-STOKES LIMIT 79 4.1
CONVERGENCE RESULT : FROM THE BOLTZMANN EQUATION T CONTENTS XI 4.4
TAKING INTO ACCOUNT BOUNDARY CONDITIONS 111 4.4.1 A PRIORI ESTIMATES
COMING FROM THE INSIDE 112 4.4.2 A PRIORI ESTIMATES COMING FROM THE
BOUNDARY 115 4.4.3 THE LIMITING BOUNDARY CONDITIONS 117 5 THE
INCOMPRESSIBLE EULER LIMIT 121 5.1 CONVERGENCE RESULT : FROM THE
BOLTZMANN EQUATION TO THE INCOMPRESSIBLE EULER SYSTEM 121 5.1.1
MATHEMATICAL THEORIES FOR THE INCOMPRESSIBLE EULER EQUATIONS 121 5.1.2
ANALOGIES WITH THE SCALED BOLTZMANN EQUATION 126 5.1.3 THE CONVERGENCE
RESULTS FOR WELL-PREPARED INITIAL DATA 127 5.1.4 THE CONVERGENCE
RESULT FOR GENERAL INITIAL DATA 129 5.2 THE RELATIVE ENTROPY METHOD 131
5.2.1 DESCRIPTION OF THE STRATEGY 131 5.2.2 THE STABILITY INEQUALITY IN
THE FRAMEWORK OF RENORMALIZED SOLUTIONS 134 5.2.3 THE STABILITY
INEQUALITY UNDER THE ADDITIONAL INTEGRABILITY ASSUMPTION 136 5.3 THE
CASE OF WELL-PREPARED INITIAL DATA 139 5.3.1 CONTROL OF THE FLUX TERM
139 5.3.2 PROOF OF THEOREM 5.1.8 AND COROLLARY 5.1.9 143 5.4 TAKING INTO
ACCOUNT ACOUSTIC WAVES 145 5.4.1 CONSTRUCTION OF APPROXIMATE SOLUTIONS
BY A FILTERING METHOD 146 5.4.2 CONTROL OF THE FLUX TERM AND PROOF OF
CONVERGENCE ... 151 5.5 TAKING INTO ACCOUNT THE KNUDSEN LAYER 155 5.5.1
THE REFINED STABILITY INEQUALITY 156 5.5.2 CONSTRUCTION OF AN
APPROXIMATE SOLUTION 158 5.5.3 CONTROL OF THE FLUX TERM AND PROOF OF
CONVERGENCE . . . 160 6 XII CONTENTS B CLASSICAL TRACE RESULTS ON THE
SOLUTIONS OF TRANSPORT EQUATIONS 171 B.L DEFINITION OF THE TRACE 172 B.2
FREE TRANSPORT WITH REFLECTION AT THE BOUNDARY 172 C SOME CONSEQUENCES
OF CHACON S BITING LEMMA 174 C.L FROM RENORMALIZED CONVERGENCE TO
CHACON S CONVERGENCE 174 C.2 A RESULT OF PARTIAL EQUIINTEGRABILITY 176
REFERENCES 181 INDEX 187
|
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| spelling | Saint-Raymond, Laure Verfasser (DE-588)135780594 aut Hydrodynamic limits of the Boltzmann equation Laure Saint-Raymond Berlin [u.a.] Springer 2009 XII, 188 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1971 Literaturverz. S. 181 - 186 Boltzmann-Gleichung - Hydrodynamischer Limes Fluides, Dynamique des - Mathématiques Maxwell-Boltzmann, Distribution de Mathematik Fluid dynamics Mathematics Maxwell-Boltzmann distribution law Boltzmann-Gleichung (DE-588)4146261-0 gnd rswk-swf Hydrodynamischer Limes (DE-588)4845720-6 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Boltzmann-Gleichung (DE-588)4146261-0 s Hydrodynamischer Limes (DE-588)4845720-6 s DE-604 Erscheint auch als Online-Ausgabe 978-3-540-92847-8 Lecture notes in mathematics 1971 (DE-604)BV000676446 1971 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017375024&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Saint-Raymond, Laure Hydrodynamic limits of the Boltzmann equation Lecture notes in mathematics Boltzmann-Gleichung - Hydrodynamischer Limes Fluides, Dynamique des - Mathématiques Maxwell-Boltzmann, Distribution de Mathematik Fluid dynamics Mathematics Maxwell-Boltzmann distribution law Boltzmann-Gleichung (DE-588)4146261-0 gnd Hydrodynamischer Limes (DE-588)4845720-6 gnd |
| subject_GND | (DE-588)4146261-0 (DE-588)4845720-6 (DE-588)1071861417 |
| title | Hydrodynamic limits of the Boltzmann equation |
| title_auth | Hydrodynamic limits of the Boltzmann equation |
| title_exact_search | Hydrodynamic limits of the Boltzmann equation |
| title_full | Hydrodynamic limits of the Boltzmann equation Laure Saint-Raymond |
| title_fullStr | Hydrodynamic limits of the Boltzmann equation Laure Saint-Raymond |
| title_full_unstemmed | Hydrodynamic limits of the Boltzmann equation Laure Saint-Raymond |
| title_short | Hydrodynamic limits of the Boltzmann equation |
| title_sort | hydrodynamic limits of the boltzmann equation |
| topic | Boltzmann-Gleichung - Hydrodynamischer Limes Fluides, Dynamique des - Mathématiques Maxwell-Boltzmann, Distribution de Mathematik Fluid dynamics Mathematics Maxwell-Boltzmann distribution law Boltzmann-Gleichung (DE-588)4146261-0 gnd Hydrodynamischer Limes (DE-588)4845720-6 gnd |
| topic_facet | Boltzmann-Gleichung - Hydrodynamischer Limes Fluides, Dynamique des - Mathématiques Maxwell-Boltzmann, Distribution de Mathematik Fluid dynamics Mathematics Maxwell-Boltzmann distribution law Boltzmann-Gleichung Hydrodynamischer Limes Konferenzschrift |
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