A RIGOROUS FORMULATION OF THE COSMOLOGICAL NEWTONIAN LIMIT WITHOUT AVERAGING

Name: Work Video:
Duration: 3 min 30 s
Description: We prove the existence of a large class of one-parameter families of cosmological solutions to the Einstein-Euler equations that have a Newtonian limit. This class includes solutions that represent a finite, but otherwise arbitrary, number of compact fluid bodies. These solutions provide exact cosmological models that admit Newtonian limits but, are not, either implicitly or explicitly, averaged.
Todd A. Oliynyk
{'id': 'https://openalex.org/W1965864915', 'doi': 'https://doi.org/10.1142/s0219891610002189', 'title': 'A RIGOROUS FORMULATION OF THE COSMOLOGICAL NEWTONIAN LIMIT WITHOUT AVERAGING', 'display_name': 'A RIGOROUS FORMULATION OF THE COSMOLOGICAL NEWTONIAN LIMIT WITHOUT AVERAGING', 'publication_year': 2010, 'publication_date': '2010-09-01', 'ids': {'openalex': 'https://openalex.org/W1965864915', 'doi': 'https://doi.org/10.1142/s0219891610002189', 'mag': '1965864915'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1142/s0219891610002189', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S18595207', 'display_name': 'Journal of Hyperbolic Differential Equations', 'issn_l': '0219-8916', 'issn': ['0219-8916', '1793-6993'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319815', 'host_organization_name': 'World Scientific', 'host_organization_lineage': ['https://openalex.org/P4310319815'], 'host_organization_lineage_names': ['World Scientific'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['arxiv', 'crossref', 'datacite'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'http://arxiv.org/pdf/0908.4454', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5007227171', 'display_name': 'Todd A. Oliynyk', 'orcid': 'https://orcid.org/0000-0003-3457-9578'}, 'institutions': [{'id': 'https://openalex.org/I56590836', 'display_name': 'Monash University', 'ror': 'https://ror.org/02bfwt286', 'country_code': 'AU', 'type': 'education', 'lineage': ['https://openalex.org/I56590836']}], 'countries': ['AU'], 'is_corresponding': True, 'raw_author_name': 'TODD A. OLIYNYK', 'raw_affiliation_strings': ['School of Mathematical Sciences , Monash University , VIC 3800, Australia'], 'affiliations': [{'raw_affiliation_string': 'School of Mathematical Sciences , Monash University , VIC 3800, Australia', 'institution_ids': ['https://openalex.org/I56590836']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5007227171'], 'corresponding_institution_ids': ['https://openalex.org/I56590836'], 'apc_list': None, 'apc_paid': None, 'fwci': 0.309, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 10, 'citation_normalized_percentile': {'value': 0.787811, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 84, 'max': 85}, 'biblio': {'volume': '07', 'issue': '03', 'first_page': '405', 'last_page': '431'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10095', 'display_name': 'Cosmology and Gravitation Theories', 'score': 0.998, 'subfield': {'id': 'https://openalex.org/subfields/3103', 'display_name': 'Astronomy and Astrophysics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T10095', 'display_name': 'Cosmology and Gravitation Theories', 'score': 0.998, 'subfield': {'id': 'https://openalex.org/subfields/3103', 'display_name': 'Astronomy and Astrophysics'}, 'field': {'id': 'https://openalex.org/fields/31', 'display_name': 'Physics and Astronomy'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10940', 'display_name': 'Navier-Stokes equation solutions', 'score': 0.9954, 'subfield': {'id': 'https://openalex.org/subfields/2604', 'display_name': 'Applied Mathematics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10229', 'display_name': 'Geometric Analysis and Curvature Flows', 'score': 0.975, 'subfield': {'id': 'https://openalex.org/subfields/2604', 'display_name': 'Applied Mathematics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/newtonian-limit', 'display_name': 'Newtonian limit', 'score': 0.73878646}], 'concepts': [{'id': 'https://openalex.org/C151201525', 'wikidata': 'https://www.wikidata.org/wiki/Q177239', 'display_name': 'Limit (mathematics)', 'level': 2, 'score': 0.75853014}, {'id': 'https://openalex.org/C2778654791', 'wikidata': 'https://www.wikidata.org/wiki/Q7020536', 'display_name': 'Newtonian limit', 'level': 3, 'score': 0.73878646}, {'id': 'https://openalex.org/C294558', 'wikidata': 'https://www.wikidata.org/wiki/Q366968', 'display_name': 'Newtonian fluid', 'level': 2, 'score': 0.7232844}, {'id': 'https://openalex.org/C2777212361', 'wikidata': 'https://www.wikidata.org/wiki/Q5127848', 'display_name': 'Class (philosophy)', 'level': 2, 'score': 0.64417195}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.6154804}, {'id': 'https://openalex.org/C38409319', 'wikidata': 'https://www.wikidata.org/wiki/Q375175', 'display_name': 'Euler equations', 'level': 2, 'score': 0.5246004}, {'id': 'https://openalex.org/C146846114', 'wikidata': 'https://www.wikidata.org/wiki/Q901448', 'display_name': 'Einstein', 'level': 2, 'score': 0.4994452}, {'id': 'https://openalex.org/C62884695', 'wikidata': 'https://www.wikidata.org/wiki/Q184871', 'display_name': "Euler's formula", 'level': 2, 'score': 0.49720052}, {'id': 'https://openalex.org/C84403224', 'wikidata': 'https://www.wikidata.org/wiki/Q860589', 'display_name': 'Non-Newtonian fluid', 'level': 2, 'score': 0.43981972}, {'id': 'https://openalex.org/C33332235', 'wikidata': 'https://www.wikidata.org/wiki/Q18362', 'display_name': 'Theoretical physics', 'level': 1, 'score': 0.38546276}, {'id': 'https://openalex.org/C74650414', 'wikidata': 'https://www.wikidata.org/wiki/Q11397', 'display_name': 'Classical mechanics', 'level': 1, 'score': 0.38313293}, {'id': 'https://openalex.org/C37914503', 'wikidata': 'https://www.wikidata.org/wiki/Q156495', 'display_name': 'Mathematical physics', 'level': 1, 'score': 0.367419}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.32868558}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.30105275}, {'id': 'https://openalex.org/C57879066', 'wikidata': 'https://www.wikidata.org/wiki/Q41217', 'display_name': 'Mechanics', 'level': 1, 'score': 0.1458123}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.084385246}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.079010755}, {'id': 'https://openalex.org/C154945302', 'wikidata': 'https://www.wikidata.org/wiki/Q11660', 'display_name': 'Artificial intelligence', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 5, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1142/s0219891610002189', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S18595207', 'display_name': 'Journal of Hyperbolic Differential Equations', 'issn_l': '0219-8916', 'issn': ['0219-8916', '1793-6993'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319815', 'host_organization_name': 'World Scientific', 'host_organization_lineage': ['https://openalex.org/P4310319815'], 'host_organization_lineage_names': ['World Scientific'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/0908.4454', 'pdf_url': 'http://arxiv.org/pdf/0908.4454', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/0908.4454', 'pdf_url': 'https://arxiv.org/pdf/0908.4454', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': None, 'pdf_url': 'https://arxiv.org/pdf/0908.4454v1.pdf', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.0908.4454', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/0908.4454', 'pdf_url': 'http://arxiv.org/pdf/0908.4454', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': ['https://openalex.org/W1965864915', 'https://openalex.org/W3098246666'], 'referenced_works_count': 17, 'referenced_works': ['https://openalex.org/W1048045440', 'https://openalex.org/W1485936747', 'https://openalex.org/W1555674425', 'https://openalex.org/W1968141139', 'https://openalex.org/W2000585298', 'https://openalex.org/W2005747825', 'https://openalex.org/W2010258025', 'https://openalex.org/W2029142535', 'https://openalex.org/W2040308657', 'https://openalex.org/W2043413393', 'https://openalex.org/W2075750897', 'https://openalex.org/W2463116024', 'https://openalex.org/W2480404596', 'https://openalex.org/W2963708297', 'https://openalex.org/W3098529974', 'https://openalex.org/W4240361988', 'https://openalex.org/W612220516'], 'related_works': ['https://openalex.org/W4377038149', 'https://openalex.org/W3180443531', 'https://openalex.org/W2950491349', 'https://openalex.org/W2412209297', 'https://openalex.org/W2315658369', 'https://openalex.org/W2267170039', 'https://openalex.org/W2119517210', 'https://openalex.org/W2087606275', 'https://openalex.org/W2055293444', 'https://openalex.org/W2051136817'], 'abstract_inverted_index': {'We': [0], 'prove': [1], 'the': [2, 15], 'existence': [3], 'of': [4, 8, 11, 35], 'a': [5, 20, 29], 'large': [6], 'class': [7, 24], 'one-parameter': [9], 'families': [10], 'cosmological': [12, 43], 'solutions': [13, 26, 40], 'to': [14], 'Einstein-Euler': [16], 'equations': [17], 'that': [18, 27, 45], 'have': [19], 'Newtonian': [21, 47], 'limit.': [22], 'This': [23], 'includes': [25], 'represent': [28], 'finite,': [30], 'but': [31], 'otherwise': [32], 'arbitrary,': [33], 'number': [34], 'compact': [36], 'fluid': [37], 'bodies.': [38], 'These': [39], 'provide': [41], 'exact': [42], 'models': [44], 'admit': [46], 'limits': [48], 'but,': [49], 'are': [50], 'not,': [51], 'either': [52], 'implicitly': [53], 'or': [54], 'explicitly,': [55], 'averaged.': [56]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1965864915', 'counts_by_year': [{'year': 2024, 'cited_by_count': 1}, {'year': 2021, 'cited_by_count': 1}, {'year': 2019, 'cited_by_count': 1}, {'year': 2018, 'cited_by_count': 2}, {'year': 2017, 'cited_by_count': 1}, {'year': 2015, 'cited_by_count': 1}, {'year': 2014, 'cited_by_count': 1}, {'year': 2012, 'cited_by_count': 1}], 'updated_date': '2025-01-04T14:37:55.375074', 'created_date': '2016-06-24'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
