Vanishing Mach Number Limit of Stochastic Compressible Flows Article Swipe

PDF

Gui‐Qiang Chen , Michele Coti Zelati , Chin Ching Yeung ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2311.14660

We study the vanishing Mach number limit for the stochastic Navier-Stokes equations with $γ$-type pressure laws, with focus on the one-dimensional case. We prove that, if the stochastic term vanishes with respect to the Mach number sufficiently fast, the deviation from the incompressible state of the solutions (for $γ\geq 1$) and the invariant measures (for $γ= 1$) is governed by a linear stochastic acoustic system in the limit. In particular, the critically sufficient decay rate for the stochastic term is slower than the corresponding results with deterministic external forcing due to the martingale structure of the noise term, and the blow-up of the noise term for the fluctuation system can be allowed.

Related Topics

Mach Number

Mathematics

Martingale (Probability Theory)

Compressibility Factor

Mathematical Analysis

Physics

Quantum Mechanics

Concepts

Mach number Mathematics Limit (mathematics) Term (time) Martingale (probability theory) Compressibility Mathematical analysis Compressible flow Physics Applied mathematics Mechanics Quantum mechanics

Metadata

Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2311.14660
PDF: https://arxiv.org/pdf/2311.14660
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4389073369

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4389073369

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.2311.14660

Digital Object Identifier
Title: Vanishing Mach Number Limit of Stochastic Compressible Flows

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2023

Year of publication
Publication date: 2023-11-24

Full publication date if available
Authors: Gui‐Qiang Chen, Michele Coti Zelati, Chin Ching Yeung

List of authors in order
Landing page: https://arxiv.org/abs/2311.14660

Publisher landing page
PDF URL: https://arxiv.org/pdf/2311.14660

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://arxiv.org/pdf/2311.14660

Direct OA link when available
Concepts: Mach number, Mathematics, Limit (mathematics), Term (time), Martingale (probability theory), Compressibility, Mathematical analysis, Compressible flow, Physics, Applied mathematics, Mechanics, Quantum mechanics

Top concepts (fields/topics) attached by OpenAlex
Cited by: 0

Total citation count in OpenAlex
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4389073369
doi	https://doi.org/10.48550/arxiv.2311.14660
ids.doi	https://doi.org/10.48550/arxiv.2311.14660
ids.openalex	https://openalex.org/W4389073369
fwci
type	preprint
title	Vanishing Mach Number Limit of Stochastic Compressible Flows
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T10067
topics[0].field.id	https://openalex.org/fields/20
topics[0].field.display_name	Economics, Econometrics and Finance
topics[0].score	0.9926999807357788
topics[0].domain.id	https://openalex.org/domains/2
topics[0].domain.display_name	Social Sciences
topics[0].subfield.id	https://openalex.org/subfields/2003
topics[0].subfield.display_name	Finance
topics[0].display_name	Stochastic processes and financial applications
topics[1].id	https://openalex.org/T10360
topics[1].field.id	https://openalex.org/fields/22
topics[1].field.display_name	Engineering
topics[1].score	0.9887999892234802
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2206
topics[1].subfield.display_name	Computational Mechanics
topics[1].display_name	Fluid Dynamics and Turbulent Flows
topics[2].id	https://openalex.org/T10940
topics[2].field.id	https://openalex.org/fields/26
topics[2].field.display_name	Mathematics
topics[2].score	0.9855999946594238
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/2604
topics[2].subfield.display_name	Applied Mathematics
topics[2].display_name	Navier-Stokes equation solutions
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C165231844
concepts[0].level	2
concepts[0].score	0.8487440347671509
concepts[0].wikidata	https://www.wikidata.org/wiki/Q160669
concepts[0].display_name	Mach number
concepts[1].id	https://openalex.org/C33923547
concepts[1].level	0
concepts[1].score	0.6102286577224731
concepts[1].wikidata	https://www.wikidata.org/wiki/Q395
concepts[1].display_name	Mathematics
concepts[2].id	https://openalex.org/C151201525
concepts[2].level	2
concepts[2].score	0.5531541109085083
concepts[2].wikidata	https://www.wikidata.org/wiki/Q177239
concepts[2].display_name	Limit (mathematics)
concepts[3].id	https://openalex.org/C61797465
concepts[3].level	2
concepts[3].score	0.5199893116950989
concepts[3].wikidata	https://www.wikidata.org/wiki/Q1188986
concepts[3].display_name	Term (time)
concepts[4].id	https://openalex.org/C48406656
concepts[4].level	2
concepts[4].score	0.5093024969100952
concepts[4].wikidata	https://www.wikidata.org/wiki/Q534112
concepts[4].display_name	Martingale (probability theory)
concepts[5].id	https://openalex.org/C84655787
concepts[5].level	2
concepts[5].score	0.48865988850593567
concepts[5].wikidata	https://www.wikidata.org/wiki/Q8067817
concepts[5].display_name	Compressibility
concepts[6].id	https://openalex.org/C134306372
concepts[6].level	1
concepts[6].score	0.44163161516189575
concepts[6].wikidata	https://www.wikidata.org/wiki/Q7754
concepts[6].display_name	Mathematical analysis
concepts[7].id	https://openalex.org/C5192115
concepts[7].level	3
concepts[7].score	0.42835551500320435
concepts[7].wikidata	https://www.wikidata.org/wiki/Q2705141
concepts[7].display_name	Compressible flow
concepts[8].id	https://openalex.org/C121332964
concepts[8].level	0
concepts[8].score	0.35864168405532837
concepts[8].wikidata	https://www.wikidata.org/wiki/Q413
concepts[8].display_name	Physics
concepts[9].id	https://openalex.org/C28826006
concepts[9].level	1
concepts[9].score	0.28435587882995605
concepts[9].wikidata	https://www.wikidata.org/wiki/Q33521
concepts[9].display_name	Applied mathematics
concepts[10].id	https://openalex.org/C57879066
concepts[10].level	1
concepts[10].score	0.12041383981704712
concepts[10].wikidata	https://www.wikidata.org/wiki/Q41217
concepts[10].display_name	Mechanics
concepts[11].id	https://openalex.org/C62520636
concepts[11].level	1
concepts[11].score	0.05750805139541626
concepts[11].wikidata	https://www.wikidata.org/wiki/Q944
concepts[11].display_name	Quantum mechanics
keywords[0].id	https://openalex.org/keywords/mach-number
keywords[0].score	0.8487440347671509
keywords[0].display_name	Mach number
keywords[1].id	https://openalex.org/keywords/mathematics
keywords[1].score	0.6102286577224731
keywords[1].display_name	Mathematics
keywords[2].id	https://openalex.org/keywords/limit
keywords[2].score	0.5531541109085083
keywords[2].display_name	Limit (mathematics)
keywords[3].id	https://openalex.org/keywords/term
keywords[3].score	0.5199893116950989
keywords[3].display_name	Term (time)
keywords[4].id	https://openalex.org/keywords/martingale
keywords[4].score	0.5093024969100952
keywords[4].display_name	Martingale (probability theory)
keywords[5].id	https://openalex.org/keywords/compressibility
keywords[5].score	0.48865988850593567
keywords[5].display_name	Compressibility
keywords[6].id	https://openalex.org/keywords/mathematical-analysis
keywords[6].score	0.44163161516189575
keywords[6].display_name	Mathematical analysis
keywords[7].id	https://openalex.org/keywords/compressible-flow
keywords[7].score	0.42835551500320435
keywords[7].display_name	Compressible flow
keywords[8].id	https://openalex.org/keywords/physics
keywords[8].score	0.35864168405532837
keywords[8].display_name	Physics
keywords[9].id	https://openalex.org/keywords/applied-mathematics
keywords[9].score	0.28435587882995605
keywords[9].display_name	Applied mathematics
keywords[10].id	https://openalex.org/keywords/mechanics
keywords[10].score	0.12041383981704712
keywords[10].display_name	Mechanics
keywords[11].id	https://openalex.org/keywords/quantum-mechanics
keywords[11].score	0.05750805139541626
keywords[11].display_name	Quantum mechanics
language	en
locations[0].id	pmh:oai:arXiv.org:2311.14660
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4306400194
locations[0].source.issn
locations[0].source.type	repository
locations[0].source.is_oa	True
locations[0].source.issn_l
locations[0].source.is_core	False
locations[0].source.is_in_doaj	False
locations[0].source.display_name	arXiv (Cornell University)
locations[0].source.host_organization	https://openalex.org/I205783295
locations[0].source.host_organization_name	Cornell University
locations[0].source.host_organization_lineage	https://openalex.org/I205783295
locations[0].license
locations[0].pdf_url	https://arxiv.org/pdf/2311.14660
locations[0].version	submittedVersion
locations[0].raw_type	text
locations[0].license_id
locations[0].is_accepted	False
locations[0].is_published	False
locations[0].raw_source_name
locations[0].landing_page_url	http://arxiv.org/abs/2311.14660
locations[1].id	doi:10.48550/arxiv.2311.14660
locations[1].is_oa	True
locations[1].source.id	https://openalex.org/S4306400194
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	True
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	arXiv (Cornell University)
locations[1].source.host_organization	https://openalex.org/I205783295
locations[1].source.host_organization_name	Cornell University
locations[1].source.host_organization_lineage	https://openalex.org/I205783295
locations[1].license	cc-by
locations[1].pdf_url
locations[1].version
locations[1].raw_type	article
locations[1].license_id	https://openalex.org/licenses/cc-by
locations[1].is_accepted	False
locations[1].is_published
locations[1].raw_source_name
locations[1].landing_page_url	https://doi.org/10.48550/arxiv.2311.14660
indexed_in	arxiv, datacite
authorships[0].author.id	https://openalex.org/A5018452636
authorships[0].author.orcid	https://orcid.org/0000-0001-5146-3839
authorships[0].author.display_name	Gui‐Qiang Chen
authorships[0].author_position	first
authorships[0].raw_author_name	Chen, Gui-Qiang G.
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5065122455
authorships[1].author.orcid	https://orcid.org/0000-0002-2495-2212
authorships[1].author.display_name	Michele Coti Zelati
authorships[1].author_position	middle
authorships[1].raw_author_name	Zelati, Michele Coti
authorships[1].is_corresponding	False
authorships[2].author.id	https://openalex.org/A5113056155
authorships[2].author.orcid
authorships[2].author.display_name	Chin Ching Yeung
authorships[2].author_position	last
authorships[2].raw_author_name	Yeung, Chin Ching
authorships[2].is_corresponding	False
has_content.pdf	False
has_content.grobid_xml	False
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://arxiv.org/pdf/2311.14660
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Vanishing Mach Number Limit of Stochastic Compressible Flows
has_fulltext	False
is_retracted	False
updated_date	2025-11-06T06:51:31.235846
primary_topic.id	https://openalex.org/T10067
primary_topic.field.id	https://openalex.org/fields/20
primary_topic.field.display_name	Economics, Econometrics and Finance
primary_topic.score	0.9926999807357788
primary_topic.domain.id	https://openalex.org/domains/2
primary_topic.domain.display_name	Social Sciences
primary_topic.subfield.id	https://openalex.org/subfields/2003
primary_topic.subfield.display_name	Finance
primary_topic.display_name	Stochastic processes and financial applications
related_works	https://openalex.org/W2003759032, https://openalex.org/W2886057782, https://openalex.org/W1999987928, https://openalex.org/W2613344690, https://openalex.org/W1650570090, https://openalex.org/W2088380080, https://openalex.org/W1986795238, https://openalex.org/W3182950612, https://openalex.org/W2995784041, https://openalex.org/W2188135746
cited_by_count	0
locations_count	2
best_oa_location.id	pmh:oai:arXiv.org:2311.14660
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4306400194
best_oa_location.source.issn
best_oa_location.source.type	repository
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l
best_oa_location.source.is_core	False
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	arXiv (Cornell University)
best_oa_location.source.host_organization	https://openalex.org/I205783295
best_oa_location.source.host_organization_name	Cornell University
best_oa_location.source.host_organization_lineage	https://openalex.org/I205783295
best_oa_location.license
best_oa_location.pdf_url	https://arxiv.org/pdf/2311.14660
best_oa_location.version	submittedVersion
best_oa_location.raw_type	text
best_oa_location.license_id
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name
best_oa_location.landing_page_url	http://arxiv.org/abs/2311.14660
primary_location.id	pmh:oai:arXiv.org:2311.14660
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4306400194
primary_location.source.issn
primary_location.source.type	repository
primary_location.source.is_oa	True
primary_location.source.issn_l
primary_location.source.is_core	False
primary_location.source.is_in_doaj	False
primary_location.source.display_name	arXiv (Cornell University)
primary_location.source.host_organization	https://openalex.org/I205783295
primary_location.source.host_organization_name	Cornell University
primary_location.source.host_organization_lineage	https://openalex.org/I205783295
primary_location.license
primary_location.pdf_url	https://arxiv.org/pdf/2311.14660
primary_location.version	submittedVersion
primary_location.raw_type	text
primary_location.license_id
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name
primary_location.landing_page_url	http://arxiv.org/abs/2311.14660
publication_date	2023-11-24
publication_year	2023
referenced_works_count	0
abstract_inverted_index.a	60
abstract_inverted_index.In	68
abstract_inverted_index.We	0, 22
abstract_inverted_index.be	110
abstract_inverted_index.by	59
abstract_inverted_index.if	25
abstract_inverted_index.in	65
abstract_inverted_index.is	57, 79
abstract_inverted_index.of	44, 94, 101
abstract_inverted_index.on	18
abstract_inverted_index.to	32, 90
abstract_inverted_index.1$)	49, 56
abstract_inverted_index.and	50, 98
abstract_inverted_index.can	109
abstract_inverted_index.due	89
abstract_inverted_index.for	7, 75, 105
abstract_inverted_index.the	2, 8, 19, 26, 33, 38, 41, 45, 51, 66, 70, 76, 82, 91, 95, 99, 102, 106
abstract_inverted_index.$γ=	55
abstract_inverted_index.(for	47, 54
abstract_inverted_index.Mach	4, 34
abstract_inverted_index.from	40
abstract_inverted_index.rate	74
abstract_inverted_index.term	28, 78, 104
abstract_inverted_index.than	81
abstract_inverted_index.with	12, 16, 30, 85
abstract_inverted_index.case.	21
abstract_inverted_index.decay	73
abstract_inverted_index.fast,	37
abstract_inverted_index.focus	17
abstract_inverted_index.laws,	15
abstract_inverted_index.limit	6
abstract_inverted_index.noise	96, 103
abstract_inverted_index.prove	23
abstract_inverted_index.state	43
abstract_inverted_index.study	1
abstract_inverted_index.term,	97
abstract_inverted_index.that,	24
abstract_inverted_index.limit.	67
abstract_inverted_index.linear	61
abstract_inverted_index.number	5, 35
abstract_inverted_index.slower	80
abstract_inverted_index.system	64, 108
abstract_inverted_index.$γ\geq	48
abstract_inverted_index.blow-up	100
abstract_inverted_index.forcing	88
abstract_inverted_index.respect	31
abstract_inverted_index.results	84
abstract_inverted_index.acoustic	63
abstract_inverted_index.allowed.	111
abstract_inverted_index.external	87
abstract_inverted_index.governed	58
abstract_inverted_index.measures	53
abstract_inverted_index.pressure	14
abstract_inverted_index.vanishes	29
abstract_inverted_index.$γ$-type	13
abstract_inverted_index.deviation	39
abstract_inverted_index.equations	11
abstract_inverted_index.invariant	52
abstract_inverted_index.solutions	46
abstract_inverted_index.structure	93
abstract_inverted_index.vanishing	3
abstract_inverted_index.critically	71
abstract_inverted_index.martingale	92
abstract_inverted_index.stochastic	9, 27, 62, 77
abstract_inverted_index.sufficient	72
abstract_inverted_index.fluctuation	107
abstract_inverted_index.particular,	69
abstract_inverted_index.sufficiently	36
abstract_inverted_index.Navier-Stokes	10
abstract_inverted_index.corresponding	83
abstract_inverted_index.deterministic	86
abstract_inverted_index.incompressible	42
abstract_inverted_index.one-dimensional	20
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	3
citation_normalized_percentile