Macroscopic Limits of Kinetic Equations View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1991

AUTHORS

Claude Bardos , François Golse , David Levermore

ABSTRACT

The connection between kinetic theory and the macroscopic equations of fluid dynamics is described. In particular, our results concerning the incompressible Navier-Stokes equation are compared with the classical derivation of Hilbert and Chapman-Enskog. Some indications of the validity of these limits are given. More specifically, the connection between the DiPerna-Lions renormalized solution for the Boltzmann equation and the Leray-Hopf solution for the Navier-Stokes equation is considered. More... »

PAGES

1-12

Book

TITLE

Multidimensional Hyperbolic Problems and Computations

ISBN

978-1-4613-9123-4
978-1-4613-9121-0

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4613-9121-0_1

DOI

http://dx.doi.org/10.1007/978-1-4613-9121-0_1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1031612892


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "familyName": "Bardos", 
        "givenName": "Claude", 
        "id": "sg:person.014224365351.76", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014224365351.76"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Paris Diderot University", 
          "id": "https://www.grid.ac/institutes/grid.7452.4", 
          "name": [
            "D\u00e9partement de Math\u00e9matiques, Universit\u00e9 Paris VII, 75251\u00a0Paris C\u00e9dex 05, France"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Golse", 
        "givenName": "Fran\u00e7ois", 
        "id": "sg:person.015753012636.03", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015753012636.03"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Arizona", 
          "id": "https://www.grid.ac/institutes/grid.134563.6", 
          "name": [
            "Department of Mathematics, University of Arizona, Tucson, Arizona\u00a085721, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Levermore", 
        "givenName": "David", 
        "id": "sg:person.014173467443.78", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014173467443.78"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/0022-1236(88)90051-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022007736"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01982349", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1024608912", 
          "https://doi.org/10.1007/bf01982349"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01982349", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1024608912", 
          "https://doi.org/10.1007/bf01982349"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01609490", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1024924697", 
          "https://doi.org/10.1007/bf01609490"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01609490", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1024924697", 
          "https://doi.org/10.1007/bf01609490"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02547354", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1026181143", 
          "https://doi.org/10.1007/bf02547354"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01210741", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027192017", 
          "https://doi.org/10.1007/bf01210741"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01210741", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027192017", 
          "https://doi.org/10.1007/bf01210741"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160330506", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1034241907"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/cpa.3160330506", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1034241907"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/1971423", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069676692"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1991", 
    "datePublishedReg": "1991-01-01", 
    "description": "The connection between kinetic theory and the macroscopic equations of fluid dynamics is described. In particular, our results concerning the incompressible Navier-Stokes equation are compared with the classical derivation of Hilbert and Chapman-Enskog. Some indications of the validity of these limits are given. More specifically, the connection between the DiPerna-Lions renormalized solution for the Boltzmann equation and the Leray-Hopf solution for the Navier-Stokes equation is considered.", 
    "editor": [
      {
        "familyName": "Glimm", 
        "givenName": "James", 
        "type": "Person"
      }, 
      {
        "familyName": "Majda", 
        "givenName": "Andrew J.", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-1-4613-9121-0_1", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-1-4613-9123-4", 
        "978-1-4613-9121-0"
      ], 
      "name": "Multidimensional Hyperbolic Problems and Computations", 
      "type": "Book"
    }, 
    "name": "Macroscopic Limits of Kinetic Equations", 
    "pagination": "1-12", 
    "productId": [
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-1-4613-9121-0_1"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "9698e9f11033cda14ef6ae1a2d3a55cb137ed32da5f6452f934f14ff719eb7ce"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1031612892"
        ]
      }
    ], 
    "publisher": {
      "location": "New York, NY", 
      "name": "Springer New York", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-1-4613-9121-0_1", 
      "https://app.dimensions.ai/details/publication/pub.1031612892"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-15T10:35", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8659_00000262.jsonl", 
    "type": "Chapter", 
    "url": "http://link.springer.com/10.1007/978-1-4613-9121-0_1"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-1-4613-9121-0_1'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-1-4613-9121-0_1'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-1-4613-9121-0_1'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-1-4613-9121-0_1'


 

This table displays all metadata directly associated to this object as RDF triples.

111 TRIPLES      23 PREDICATES      34 URIs      20 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-1-4613-9121-0_1 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Nc45bcaa6f8f849649f9105f9d425e7c6
4 schema:citation sg:pub.10.1007/bf01210741
5 sg:pub.10.1007/bf01609490
6 sg:pub.10.1007/bf01982349
7 sg:pub.10.1007/bf02547354
8 https://doi.org/10.1002/cpa.3160330506
9 https://doi.org/10.1016/0022-1236(88)90051-1
10 https://doi.org/10.2307/1971423
11 schema:datePublished 1991
12 schema:datePublishedReg 1991-01-01
13 schema:description The connection between kinetic theory and the macroscopic equations of fluid dynamics is described. In particular, our results concerning the incompressible Navier-Stokes equation are compared with the classical derivation of Hilbert and Chapman-Enskog. Some indications of the validity of these limits are given. More specifically, the connection between the DiPerna-Lions renormalized solution for the Boltzmann equation and the Leray-Hopf solution for the Navier-Stokes equation is considered.
14 schema:editor N6faaad990f574ee4a8c1230cb7ad9727
15 schema:genre chapter
16 schema:inLanguage en
17 schema:isAccessibleForFree false
18 schema:isPartOf Nf704b9116cdd40f9a33ee492232a7c43
19 schema:name Macroscopic Limits of Kinetic Equations
20 schema:pagination 1-12
21 schema:productId N31fd725c23104df6947ba7cd68a12818
22 Nac3d5eac18f54dcfabb5021a6af18058
23 Nfd24807295d84cfa9fda6e0ed42c6d28
24 schema:publisher N7d2864a818b242749ab5a54a35b50387
25 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031612892
26 https://doi.org/10.1007/978-1-4613-9121-0_1
27 schema:sdDatePublished 2019-04-15T10:35
28 schema:sdLicense https://scigraph.springernature.com/explorer/license/
29 schema:sdPublisher N4dd75e61108640169e6efddc02d81969
30 schema:url http://link.springer.com/10.1007/978-1-4613-9121-0_1
31 sgo:license sg:explorer/license/
32 sgo:sdDataset chapters
33 rdf:type schema:Chapter
34 N1dcb0626996d4d5191ef633b77823563 schema:familyName Majda
35 schema:givenName Andrew J.
36 rdf:type schema:Person
37 N279b348a464448b4a2c1a80e7854fe3c rdf:first N1dcb0626996d4d5191ef633b77823563
38 rdf:rest rdf:nil
39 N31fd725c23104df6947ba7cd68a12818 schema:name readcube_id
40 schema:value 9698e9f11033cda14ef6ae1a2d3a55cb137ed32da5f6452f934f14ff719eb7ce
41 rdf:type schema:PropertyValue
42 N4dd75e61108640169e6efddc02d81969 schema:name Springer Nature - SN SciGraph project
43 rdf:type schema:Organization
44 N6faaad990f574ee4a8c1230cb7ad9727 rdf:first Nf71b23602ab74847b86e55b366a0b085
45 rdf:rest N279b348a464448b4a2c1a80e7854fe3c
46 N7d2864a818b242749ab5a54a35b50387 schema:location New York, NY
47 schema:name Springer New York
48 rdf:type schema:Organisation
49 Naa6938f5b53c4bc9b1881060945f646a rdf:first sg:person.014173467443.78
50 rdf:rest rdf:nil
51 Nac3d5eac18f54dcfabb5021a6af18058 schema:name dimensions_id
52 schema:value pub.1031612892
53 rdf:type schema:PropertyValue
54 Nc45bcaa6f8f849649f9105f9d425e7c6 rdf:first sg:person.014224365351.76
55 rdf:rest Nfadab3c6d3e244f0901a32b29d56369c
56 Nf704b9116cdd40f9a33ee492232a7c43 schema:isbn 978-1-4613-9121-0
57 978-1-4613-9123-4
58 schema:name Multidimensional Hyperbolic Problems and Computations
59 rdf:type schema:Book
60 Nf71b23602ab74847b86e55b366a0b085 schema:familyName Glimm
61 schema:givenName James
62 rdf:type schema:Person
63 Nfadab3c6d3e244f0901a32b29d56369c rdf:first sg:person.015753012636.03
64 rdf:rest Naa6938f5b53c4bc9b1881060945f646a
65 Nfd24807295d84cfa9fda6e0ed42c6d28 schema:name doi
66 schema:value 10.1007/978-1-4613-9121-0_1
67 rdf:type schema:PropertyValue
68 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
69 schema:name Mathematical Sciences
70 rdf:type schema:DefinedTerm
71 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
72 schema:name Pure Mathematics
73 rdf:type schema:DefinedTerm
74 sg:person.014173467443.78 schema:affiliation https://www.grid.ac/institutes/grid.134563.6
75 schema:familyName Levermore
76 schema:givenName David
77 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014173467443.78
78 rdf:type schema:Person
79 sg:person.014224365351.76 schema:familyName Bardos
80 schema:givenName Claude
81 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014224365351.76
82 rdf:type schema:Person
83 sg:person.015753012636.03 schema:affiliation https://www.grid.ac/institutes/grid.7452.4
84 schema:familyName Golse
85 schema:givenName François
86 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015753012636.03
87 rdf:type schema:Person
88 sg:pub.10.1007/bf01210741 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027192017
89 https://doi.org/10.1007/bf01210741
90 rdf:type schema:CreativeWork
91 sg:pub.10.1007/bf01609490 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024924697
92 https://doi.org/10.1007/bf01609490
93 rdf:type schema:CreativeWork
94 sg:pub.10.1007/bf01982349 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024608912
95 https://doi.org/10.1007/bf01982349
96 rdf:type schema:CreativeWork
97 sg:pub.10.1007/bf02547354 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026181143
98 https://doi.org/10.1007/bf02547354
99 rdf:type schema:CreativeWork
100 https://doi.org/10.1002/cpa.3160330506 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034241907
101 rdf:type schema:CreativeWork
102 https://doi.org/10.1016/0022-1236(88)90051-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022007736
103 rdf:type schema:CreativeWork
104 https://doi.org/10.2307/1971423 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069676692
105 rdf:type schema:CreativeWork
106 https://www.grid.ac/institutes/grid.134563.6 schema:alternateName University of Arizona
107 schema:name Department of Mathematics, University of Arizona, Tucson, Arizona 85721, USA
108 rdf:type schema:Organization
109 https://www.grid.ac/institutes/grid.7452.4 schema:alternateName Paris Diderot University
110 schema:name Département de Mathématiques, Université Paris VII, 75251 Paris Cédex 05, France
111 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...