Resolvent Estimates for the Stokes Operator in Bounded and Exterior $C^1$ Domains Article Swipe
Jun Geng
,
Zhongwei Shen
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2401.03222
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2401.03222
We establish resolvent estimates in $L^q$ spaces for the Stokes operator in a bounded $C^1$ domain $Ω$ in $\mathbb{R}^d$. As a corollary, it follows that the Stokes operator generates a bounded analytic semigroup in $L^q(Ω; \mathbb{C}^d)$ for any $1< q< \infty$ and $d\ge 2$. The case of an exterior $C^1$ domain is also studied.
Related Topics
Concepts
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2401.03222
- https://arxiv.org/pdf/2401.03222
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4390722835
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4390722835Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2401.03222Digital Object Identifier
- Title
-
Resolvent Estimates for the Stokes Operator in Bounded and Exterior $C^1$ DomainsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-01-06Full publication date if available
- Authors
-
Jun Geng, Zhongwei ShenList of authors in order
- Landing page
-
https://arxiv.org/abs/2401.03222Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2401.03222Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2401.03222Direct OA link when available
- Concepts
-
Bounded function, Resolvent, Analytic semigroup, Domain (mathematical analysis), Mathematics, Semigroup, Operator (biology), Omega, Bounded operator, Corollary, Mathematical analysis, Pure mathematics, Physics, Quantum mechanics, Repressor, Gene, Biochemistry, Chemistry, Transcription factorTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4390722835 |
|---|---|
| doi | https://doi.org/10.48550/arxiv.2401.03222 |
| ids.doi | https://doi.org/10.48550/arxiv.2401.03222 |
| ids.openalex | https://openalex.org/W4390722835 |
| fwci | |
| type | preprint |
| title | Resolvent Estimates for the Stokes Operator in Bounded and Exterior $C^1$ Domains |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T12100 |
| topics[0].field.id | https://openalex.org/fields/17 |
| topics[0].field.display_name | Computer Science |
| topics[0].score | 0.9883000254631042 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1703 |
| topics[0].subfield.display_name | Computational Theory and Mathematics |
| topics[0].display_name | Advanced Mathematical Modeling in Engineering |
| topics[1].id | https://openalex.org/T10940 |
| topics[1].field.id | https://openalex.org/fields/26 |
| topics[1].field.display_name | Mathematics |
| topics[1].score | 0.9848999977111816 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2604 |
| topics[1].subfield.display_name | Applied Mathematics |
| topics[1].display_name | Navier-Stokes equation solutions |
| topics[2].id | https://openalex.org/T11205 |
| topics[2].field.id | https://openalex.org/fields/26 |
| topics[2].field.display_name | Mathematics |
| topics[2].score | 0.9445000290870667 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2610 |
| topics[2].subfield.display_name | Mathematical Physics |
| topics[2].display_name | Numerical methods in inverse problems |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C34388435 |
| concepts[0].level | 2 |
| concepts[0].score | 0.867443323135376 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q2267362 |
| concepts[0].display_name | Bounded function |
| concepts[1].id | https://openalex.org/C196267783 |
| concepts[1].level | 2 |
| concepts[1].score | 0.8648223876953125 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q4392490 |
| concepts[1].display_name | Resolvent |
| concepts[2].id | https://openalex.org/C2779751289 |
| concepts[2].level | 3 |
| concepts[2].score | 0.7878947257995605 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q485292 |
| concepts[2].display_name | Analytic semigroup |
| concepts[3].id | https://openalex.org/C36503486 |
| concepts[3].level | 2 |
| concepts[3].score | 0.712925910949707 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q11235244 |
| concepts[3].display_name | Domain (mathematical analysis) |
| concepts[4].id | https://openalex.org/C33923547 |
| concepts[4].level | 0 |
| concepts[4].score | 0.692907452583313 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[4].display_name | Mathematics |
| concepts[5].id | https://openalex.org/C207405024 |
| concepts[5].level | 2 |
| concepts[5].score | 0.642612099647522 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q207348 |
| concepts[5].display_name | Semigroup |
| concepts[6].id | https://openalex.org/C17020691 |
| concepts[6].level | 5 |
| concepts[6].score | 0.6215254068374634 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q139677 |
| concepts[6].display_name | Operator (biology) |
| concepts[7].id | https://openalex.org/C2779557605 |
| concepts[7].level | 2 |
| concepts[7].score | 0.6014934182167053 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q9890 |
| concepts[7].display_name | Omega |
| concepts[8].id | https://openalex.org/C175454919 |
| concepts[8].level | 3 |
| concepts[8].score | 0.5864779949188232 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q2342396 |
| concepts[8].display_name | Bounded operator |
| concepts[9].id | https://openalex.org/C2780012671 |
| concepts[9].level | 2 |
| concepts[9].score | 0.5654149651527405 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q1343870 |
| concepts[9].display_name | Corollary |
| concepts[10].id | https://openalex.org/C134306372 |
| concepts[10].level | 1 |
| concepts[10].score | 0.45908015966415405 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[10].display_name | Mathematical analysis |
| concepts[11].id | https://openalex.org/C202444582 |
| concepts[11].level | 1 |
| concepts[11].score | 0.3858448565006256 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q837863 |
| concepts[11].display_name | Pure mathematics |
| concepts[12].id | https://openalex.org/C121332964 |
| concepts[12].level | 0 |
| concepts[12].score | 0.18774187564849854 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[12].display_name | Physics |
| concepts[13].id | https://openalex.org/C62520636 |
| concepts[13].level | 1 |
| concepts[13].score | 0.056437909603118896 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q944 |
| concepts[13].display_name | Quantum mechanics |
| concepts[14].id | https://openalex.org/C158448853 |
| concepts[14].level | 4 |
| concepts[14].score | 0.0 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q425218 |
| concepts[14].display_name | Repressor |
| concepts[15].id | https://openalex.org/C104317684 |
| concepts[15].level | 2 |
| concepts[15].score | 0.0 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q7187 |
| concepts[15].display_name | Gene |
| concepts[16].id | https://openalex.org/C55493867 |
| concepts[16].level | 1 |
| concepts[16].score | 0.0 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q7094 |
| concepts[16].display_name | Biochemistry |
| concepts[17].id | https://openalex.org/C185592680 |
| concepts[17].level | 0 |
| concepts[17].score | 0.0 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q2329 |
| concepts[17].display_name | Chemistry |
| concepts[18].id | https://openalex.org/C86339819 |
| concepts[18].level | 3 |
| concepts[18].score | 0.0 |
| concepts[18].wikidata | https://www.wikidata.org/wiki/Q407384 |
| concepts[18].display_name | Transcription factor |
| keywords[0].id | https://openalex.org/keywords/bounded-function |
| keywords[0].score | 0.867443323135376 |
| keywords[0].display_name | Bounded function |
| keywords[1].id | https://openalex.org/keywords/resolvent |
| keywords[1].score | 0.8648223876953125 |
| keywords[1].display_name | Resolvent |
| keywords[2].id | https://openalex.org/keywords/analytic-semigroup |
| keywords[2].score | 0.7878947257995605 |
| keywords[2].display_name | Analytic semigroup |
| keywords[3].id | https://openalex.org/keywords/domain |
| keywords[3].score | 0.712925910949707 |
| keywords[3].display_name | Domain (mathematical analysis) |
| keywords[4].id | https://openalex.org/keywords/mathematics |
| keywords[4].score | 0.692907452583313 |
| keywords[4].display_name | Mathematics |
| keywords[5].id | https://openalex.org/keywords/semigroup |
| keywords[5].score | 0.642612099647522 |
| keywords[5].display_name | Semigroup |
| keywords[6].id | https://openalex.org/keywords/operator |
| keywords[6].score | 0.6215254068374634 |
| keywords[6].display_name | Operator (biology) |
| keywords[7].id | https://openalex.org/keywords/omega |
| keywords[7].score | 0.6014934182167053 |
| keywords[7].display_name | Omega |
| keywords[8].id | https://openalex.org/keywords/bounded-operator |
| keywords[8].score | 0.5864779949188232 |
| keywords[8].display_name | Bounded operator |
| keywords[9].id | https://openalex.org/keywords/corollary |
| keywords[9].score | 0.5654149651527405 |
| keywords[9].display_name | Corollary |
| keywords[10].id | https://openalex.org/keywords/mathematical-analysis |
| keywords[10].score | 0.45908015966415405 |
| keywords[10].display_name | Mathematical analysis |
| keywords[11].id | https://openalex.org/keywords/pure-mathematics |
| keywords[11].score | 0.3858448565006256 |
| keywords[11].display_name | Pure mathematics |
| keywords[12].id | https://openalex.org/keywords/physics |
| keywords[12].score | 0.18774187564849854 |
| keywords[12].display_name | Physics |
| keywords[13].id | https://openalex.org/keywords/quantum-mechanics |
| keywords[13].score | 0.056437909603118896 |
| keywords[13].display_name | Quantum mechanics |
| language | en |
| locations[0].id | pmh:oai:arXiv.org:2401.03222 |
| 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 | cc-by |
| locations[0].pdf_url | https://arxiv.org/pdf/2401.03222 |
| locations[0].version | submittedVersion |
| locations[0].raw_type | text |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | False |
| locations[0].is_published | False |
| locations[0].raw_source_name | |
| locations[0].landing_page_url | http://arxiv.org/abs/2401.03222 |
| locations[1].id | doi:10.48550/arxiv.2401.03222 |
| 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.2401.03222 |
| indexed_in | arxiv, datacite |
| authorships[0].author.id | https://openalex.org/A5103752132 |
| authorships[0].author.orcid | |
| authorships[0].author.display_name | Jun Geng |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Geng, Jun |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5065781968 |
| authorships[1].author.orcid | https://orcid.org/0000-0003-2387-7342 |
| authorships[1].author.display_name | Zhongwei Shen |
| authorships[1].author_position | last |
| authorships[1].raw_author_name | Shen, Zhongwei |
| authorships[1].is_corresponding | False |
| has_content.pdf | True |
| has_content.grobid_xml | True |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://arxiv.org/pdf/2401.03222 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2024-01-13T00:00:00 |
| display_name | Resolvent Estimates for the Stokes Operator in Bounded and Exterior $C^1$ Domains |
| has_fulltext | True |
| is_retracted | False |
| updated_date | 2025-11-06T06:51:31.235846 |
| primary_topic.id | https://openalex.org/T12100 |
| primary_topic.field.id | https://openalex.org/fields/17 |
| primary_topic.field.display_name | Computer Science |
| primary_topic.score | 0.9883000254631042 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1703 |
| primary_topic.subfield.display_name | Computational Theory and Mathematics |
| primary_topic.display_name | Advanced Mathematical Modeling in Engineering |
| related_works | https://openalex.org/W2945455047, https://openalex.org/W2106070738, https://openalex.org/W1964813471, https://openalex.org/W2975981742, https://openalex.org/W2364132950, https://openalex.org/W1674480361, https://openalex.org/W2915024987, https://openalex.org/W1964251668, https://openalex.org/W3007534944, https://openalex.org/W1985702565 |
| cited_by_count | 0 |
| locations_count | 2 |
| best_oa_location.id | pmh:oai:arXiv.org:2401.03222 |
| 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 | cc-by |
| best_oa_location.pdf_url | https://arxiv.org/pdf/2401.03222 |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | text |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| 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/2401.03222 |
| primary_location.id | pmh:oai:arXiv.org:2401.03222 |
| 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 | cc-by |
| primary_location.pdf_url | https://arxiv.org/pdf/2401.03222 |
| primary_location.version | submittedVersion |
| primary_location.raw_type | text |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | |
| primary_location.landing_page_url | http://arxiv.org/abs/2401.03222 |
| publication_date | 2024-01-06 |
| publication_year | 2024 |
| referenced_works_count | 0 |
| abstract_inverted_index.a | 12, 20, 29 |
| abstract_inverted_index.As | 19 |
| abstract_inverted_index.We | 0 |
| abstract_inverted_index.an | 47 |
| abstract_inverted_index.in | 4, 11, 17, 33 |
| abstract_inverted_index.is | 51 |
| abstract_inverted_index.it | 22 |
| abstract_inverted_index.of | 46 |
| abstract_inverted_index.2$. | 43 |
| abstract_inverted_index.The | 44 |
| abstract_inverted_index.and | 41 |
| abstract_inverted_index.any | 37 |
| abstract_inverted_index.for | 7, 36 |
| abstract_inverted_index.the | 8, 25 |
| abstract_inverted_index.$Ω$ | 16 |
| abstract_inverted_index.also | 52 |
| abstract_inverted_index.case | 45 |
| abstract_inverted_index.that | 24 |
| abstract_inverted_index.$C^1$ | 14, 49 |
| abstract_inverted_index.$L^q$ | 5 |
| abstract_inverted_index.$d\ge | 42 |
| abstract_inverted_index.q< | 39 |
| abstract_inverted_index.$1< | 38 |
| abstract_inverted_index.Stokes | 9, 26 |
| abstract_inverted_index.domain | 15, 50 |
| abstract_inverted_index.spaces | 6 |
| abstract_inverted_index.\infty$ | 40 |
| abstract_inverted_index.bounded | 13, 30 |
| abstract_inverted_index.follows | 23 |
| abstract_inverted_index.$L^q(Ω; | 34 |
| abstract_inverted_index.analytic | 31 |
| abstract_inverted_index.exterior | 48 |
| abstract_inverted_index.operator | 10, 27 |
| abstract_inverted_index.studied. | 53 |
| abstract_inverted_index.establish | 1 |
| abstract_inverted_index.estimates | 3 |
| abstract_inverted_index.generates | 28 |
| abstract_inverted_index.resolvent | 2 |
| abstract_inverted_index.semigroup | 32 |
| abstract_inverted_index.corollary, | 21 |
| abstract_inverted_index.\mathbb{C}^d)$ | 35 |
| abstract_inverted_index.$\mathbb{R}^d$. | 18 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile |