Stochastic power law fluids: Existence and uniqueness of weak solutions

We consider a stochastic partial differential equation (SPDE) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force. Here the extra stress tensor of the fluid is given by a polynomial of degree \(p-1\) of the rate of strain tensor, while the co...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Terasawa, Yutaka, Yoshida, Nobuo
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.01.2012
Subjects
Fluid dynamics
Fluid flow
Incompressible flow
Mathematical analysis
Mathematics - Probability
Newtonian fluids
Non Newtonian fluids
Partial differential equations
Polynomials
Tensors
Uniqueness
Velocity distribution
Online AccessGet full text
ISSN2331-8422
DOI10.48550/arxiv.1002.1431

Cover

Abstract We consider a stochastic partial differential equation (SPDE) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force. Here the extra stress tensor of the fluid is given by a polynomial of degree \(p-1\) of the rate of strain tensor, while the colored noise is considered as a random force. We investigate the existence and the uniqueness of weak solutions to this SPDE.
AbstractList We consider a stochastic partial differential equation (SPDE) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force. Here the extra stress tensor of the fluid is given by a polynomial of degree \(p-1\) of the rate of strain tensor, while the colored noise is considered as a random force. We investigate the existence and the uniqueness of weak solutions to this SPDE.
Annals of Applied Probability 2011, Vol. 21, No. 5, 1827-1859 We consider a stochastic partial differential equation (SPDE) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a random force. Here the extra stress tensor of the fluid is given by a polynomial of degree $p-1$ of the rate of strain tensor, while the colored noise is considered as a random force. We investigate the existence and the uniqueness of weak solutions to this SPDE.
Author Terasawa, Yutaka
Yoshida, Nobuo
Author_xml – sequence: 1
  givenname: Yutaka
  surname: Terasawa
  fullname: Terasawa, Yutaka
– sequence: 2
  givenname: Nobuo
  surname: Yoshida
  fullname: Yoshida, Nobuo
BackLink https://doi.org/10.48550/arXiv.1002.1431$$DView paper in arXiv
https://doi.org/10.1214/10-AAP741$$DView published paper (Access to full text may be restricted)
BookMark eNotj01LAzEYhIMoWGvvniTgeWs-dxNvUmoVCh7sfXk3H5i6JnWza-u_d2uFgTnMMMxzhc5jig6hG0rmQklJ7qE7hO85JYTNqeD0DE0Y57RQgrFLNMt5S8aorJiUfIJWb30y75D7YPAu7V2HW9hj3w7B5ge8PITcu2gchmjxEMPX4KLLGSeP9w4-cE7t0IcU8zW68NBmN_v3Kdo8LTeL52L9unpZPK4LkFQXnBvRKGKlB20JJcILX1JqKwYVVN5SYxpbqcYoB7TiVakVOAqaNc0o4vkU3Z5m_yDrXRc-ofupj7D1EXYs3J0Kuy6NZ3Nfb9PQxfFSzYiSuuRCa_4LyEFZ0g
ContentType Paper
Journal Article
Copyright 2012. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
http://arxiv.org/licenses/nonexclusive-distrib/1.0
Copyright_xml – notice: 2012. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
– notice: http://arxiv.org/licenses/nonexclusive-distrib/1.0
DBID 8FE
8FG
ABJCF
ABUWG
AFKRA
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
HCIFZ
L6V
M7S
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
AKZ
GOX
DOI 10.48550/arxiv.1002.1431
DatabaseName ProQuest SciTech Collection
ProQuest Technology Collection
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
ProQuest Central Essentials
ProQuest Central
Technology Collection
ProQuest One Community College
ProQuest Central
SciTech Premium Collection
ProQuest Engineering Collection
Engineering Database
ProQuest Central Premium
ProQuest One Academic (New)
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering Collection
arXiv Mathematics
arXiv.org
DatabaseTitle Publicly Available Content Database
Engineering Database
Technology Collection
ProQuest One Academic Middle East (New)
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest Central China
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Engineering Collection
ProQuest One Academic UKI Edition
ProQuest Central Korea
Materials Science & Engineering Collection
ProQuest Central (New)
ProQuest One Academic
ProQuest One Academic (New)
Engineering Collection
DatabaseTitleList Publicly Available Content Database
Database_xml – sequence: 1
  dbid: GOX
  name: arXiv.org
  url: http://arxiv.org/find
  sourceTypes: Open Access Repository
– sequence: 2
  dbid: 8FG
  name: ProQuest Technology Collection
  url: https://search.proquest.com/technologycollection1
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Physics
EISSN 2331-8422
ExternalDocumentID 1002_1431
Genre Working Paper/Pre-Print
GroupedDBID 8FE
8FG
ABJCF
ABUWG
AFKRA
ALMA_UNASSIGNED_HOLDINGS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
FRJ
HCIFZ
L6V
M7S
M~E
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
AKZ
GOX
ID FETCH-LOGICAL-a519-33c4b80d5fa9d0104f4f611d72a7a7fd1ccbd78bc8ea1737698ae1a92bb2bb0f3
IEDL.DBID 8FG
IngestDate Tue Jul 22 23:05:39 EDT 2025
Mon Jun 30 09:25:10 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed false
IsScholarly false
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-a519-33c4b80d5fa9d0104f4f611d72a7a7fd1ccbd78bc8ea1737698ae1a92bb2bb0f3
Notes SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
IMS-AAP-AAP741
OpenAccessLink https://www.proquest.com/docview/2085963499?pq-origsite=%requestingapplication%
PQID 2085963499
PQPubID 2050157
ParticipantIDs arxiv_primary_1002_1431
proquest_journals_2085963499
PublicationCentury 2000
PublicationDate 20120104
PublicationDateYYYYMMDD 2012-01-04
PublicationDate_xml – month: 01
  year: 2012
  text: 20120104
  day: 04
PublicationDecade 2010
PublicationPlace Ithaca
PublicationPlace_xml – name: Ithaca
PublicationTitle arXiv.org
PublicationYear 2012
Publisher Cornell University Library, arXiv.org
Publisher_xml – name: Cornell University Library, arXiv.org
SSID ssj0002672553
Score 1.4757074
SecondaryResourceType preprint
Snippet We consider a stochastic partial differential equation (SPDE) which describes the velocity field of a viscous, incompressible non-Newtonian fluid subject to a...
Annals of Applied Probability 2011, Vol. 21, No. 5, 1827-1859 We consider a stochastic partial differential equation (SPDE) which describes the velocity field...
SourceID arxiv
proquest
SourceType Open Access Repository
Aggregation Database
SubjectTerms Fluid dynamics
Fluid flow
Incompressible flow
Mathematical analysis
Mathematics - Probability
Newtonian fluids
Non Newtonian fluids
Partial differential equations
Polynomials
Tensors
Uniqueness
Velocity distribution
SummonAdditionalLinks – databaseName: arXiv.org
  dbid: GOX
  link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwdV1LSwMxEA61Jy-i-KpWzcHrQpLNbrLeRPpAUA9W6G2ZbBIslrb0YfvznWTXXkQIC1lmLzOZ5JsN832E3KscMuAGEpkVKT7SLAGV4pRpL51hRkeZzpfXfPghn8fZuEXufnthYLmbfNf8wCZojjCBuRz6pA-ECLXV4G1cXzZGJq7GfG-GCDO--bOxxtOif0yOGphHH-u4nJCWm52Swft6Xn1CYEami6BORqewpX66mdjVA-3tgscxBhSLe7qJxKphH6JzT7cOvuh-lZyRUb83ehomjZBBAgiQkjStpNHMZh4KG-ofL33OuVUCFChveVUZq7SptAOuMOMLDY5DIYzBwXx6Ttqz-cxdEorghUswCMKskVxAoYBZVkEuAE2l7pCL6IByUXNVBEpiUQbXdEj31yVls0xXZRDoxAzEqufq3w-vySGCBBF_O8guaa-XG3eDB_Ha3MZw_ABRLok0
  priority: 102
  providerName: Cornell University
Title Stochastic power law fluids: Existence and uniqueness of weak solutions
URI https://www.proquest.com/docview/2085963499
https://arxiv.org/abs/1002.1431
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV3PS8MwFA66Injzt9M5cvBa1rRp03oRlG5D2Bw6Ybfx0rQ4HG3dD7eTf7svWTcPglACSXvKe3zv60v4PkJuRQA-MAk29yMPB8-3QXg4dcKMp9KRobHp7PWD7ht_GvmjquE2r65VbjHRALUqEt0jb2kvSUwWJOj35aetXaP06WplobFPLIaVRud52O7seixuIJAxe5vTSSPd1YLZevJldEcRI7SznGVW_iCxKS_tI2INoExnx2QvzU_IgbmVmcxPSed1USTvoKWUaantzOgUVjSbLidqfkfjtQ4RBo1CrujSKLFq4KJFRlcpfNBdWp2RYTsePnbtyvnABmRUtuclXIaO8jOIlP5hyngWMKaECwJEpliSSCVCmYQpMIEQEYWQMohcKfFxMu-c1PIiTy8JRbbDOEhkbUpy5kIkwFFOAoEL-CkP6-TCbMC43IhbaA1jd6y3pk4a2y0ZV3k9H_9G4er_19fkEKmFa5oVvEFqi9kyvcHyvZBNE6MmsR7i_uAFZ53nEY697_gH0KSeTg
linkProvider ProQuest
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1bS8MwFD7ohuib99vUPOhjsU3TphVEUKfzNkQn-FZOmhRF2eYuTn-U_9GTbNMHwbdBKfRCH06-nH45Sb4PYFfGGGGg0BNRGtIpjDyUIV36SSGM8lXibDpv6nHtQVw-Ro9T8DXeC2OXVY5zokvUupXbGvm-9ZIksBBBP2q_edY1ys6uji00hrC4Mp8DGrJ1Dy9OqX33OD-rNk5q3shVwENiK14Y5kIlvo4KTLUdjBSiiINAS44SZaGDPFdaJipPDAaSul-aoAkw5UrR4RchfXYaysJuaC1B-bhav737KerwWBJFD4fToU4rbB87H8_vTuiUkpK1siu7O39Sv_ufnc1D-RbbprMAU6a5CDNuGWjeXYLz-14rf0Kr3cza1j-NveKAFa_9Z909YNUPiwlCCcOmZn0n_WozJWsVbGDwhf3geBkakwjKCpSaraZZA0b0KhCoiCZqJQKOqURf-znGHOlVkazDqgtA1h6qaVjRZJ7Z0KxDZRySbNSRutlvs2_8_3gHZmuNm-vs-qJ-tQlzxGu4q5SICpR6nb7ZIu7QU9ujFmOQTRgj3y9t2WE
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Stochastic+power+law+fluids%3A+Existence+and+uniqueness+of+weak+solutions&rft.jtitle=arXiv.org&rft.au=Terasawa%2C+Yutaka&rft.au=Yoshida%2C+Nobuo&rft.date=2012-01-04&rft.pub=Cornell+University+Library%2C+arXiv.org&rft.eissn=2331-8422&rft_id=info:doi/10.48550%2Farxiv.1002.1431