{"id":"https://openalex.org/W6891277396","doi":"https://doi.org/10.3929/ethz-b-000690797","title":"Exact hydrodynamic manifolds for the linear Boltzmann BGK equation I: spectral theory","display_name":"Exact hydrodynamic manifolds for the linear Boltzmann BGK equation I: spectral theory","publication_year":2024,"publication_date":"2024-11-01","ids":{"openalex":"https://openalex.org/W6891277396","doi":"https://doi.org/10.3929/ethz-b-000690797"},"language":"en","primary_location":{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/690797","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/690797","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Continuum Mechanics and Thermodynamics, 36 (6)","raw_type":"info:eu-repo/semantics/article"},"volume":null,"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/20.500.11850/690797","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048968881","display_name":"Florian Kogelbauer","orcid":"https://orcid.org/0000-0002-2896-6435","observed_orcids":["https://orcid.org/0000-0002-2896-6435"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kogelbauer, Florian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5025331583","display_name":"Ilya V. Karlin","orcid":"https://orcid.org/0000-0001-9996-9679","observed_orcids":["https://orcid.org/0000-0001-9996-9679"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Karlin, Ilya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.41521545,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9965999722480774,"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"}},"topics":[{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9965999722480774,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/spectral-theory","display_name":"spectral theory","score":0.7639999985694885},{"id":"https://openalex.org/keywords/finite-rank-perturbations","display_name":"finite rank perturbations","score":0.9229999780654907},{"id":"https://openalex.org/keywords/critical-wave-number","display_name":"critical wave number","score":0.9419999718666077},{"id":"https://openalex.org/keywords/hydrodynamic-modes","display_name":"hydrodynamic modes","score":0.8159999847412109},{"id":"https://openalex.org/keywords/essential-spectrum","display_name":"essential spectrum","score":0.6579999923706055},{"id":"https://openalex.org/keywords/method-of-moments","display_name":"method of moments","score":0.6079999804496765},{"id":"https://openalex.org/keywords/kinetic-equations","display_name":"kinetic equations","score":0.6380000114440918}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7085999846458435},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6226000189781189},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5565000176429749},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5339999794960022},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.4837000072002411},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4778999984264374},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.47679999470710754},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4674000144004822},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.40049999952316284},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.39989998936653137},{"id":"https://openalex.org/C2983668108","wikidata":"https://www.wikidata.org/wiki/Q280453","display_name":"Spectral analysis","level":3,"score":0.3995000123977661},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3880999982357025},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.3781000077724457},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.37049999833106995},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.3698999881744385},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.3596999943256378},{"id":"https://openalex.org/C121130766","wikidata":"https://www.wikidata.org/wiki/Q192510","display_name":"Wavenumber","level":2,"score":0.349700003862381},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.34850001335144043},{"id":"https://openalex.org/C139609574","wikidata":"https://www.wikidata.org/wiki/Q2273509","display_name":"Transcendental equation","level":3,"score":0.3255000114440918},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.3109999895095825},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3057999908924103},{"id":"https://openalex.org/C186121230","wikidata":"https://www.wikidata.org/wiki/Q7575215","display_name":"Spectral theory of ordinary differential equations","level":5,"score":0.30320000648498535},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3018999993801117},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.257999986410141},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C188370112","wikidata":"https://www.wikidata.org/wiki/Q173091","display_name":"Transcendental number","level":2,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/690797","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/690797","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Continuum Mechanics and Thermodynamics, 36 (6)","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.3929/ethz-b-000690797","doi":"https://doi.org/10.3929/ethz-b-000690797","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000690797","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/690797","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/690797","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Continuum Mechanics and Thermodynamics, 36 (6)","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"perform":[1],"a":[2,33,72,79,90],"complete":[3],"spectral":[4,108],"analysis":[5],"of":[6,25,32,42,71,81,96],"the":[7,20,23,30,40,46,60,69,104,107],"linear":[8,75],"three-dimensional":[9],"Boltzmann":[10],"BGK":[11],"operator":[12],"resulting":[13],"in":[14,45],"an":[15],"explicit":[16],"transcendental":[17],"equation":[18],"for":[19,92,106],"eigenvalues.":[21],"Using":[22],"theory":[24],"finite-rank":[26],"perturbations,":[27],"we":[28],"confirm":[29],"existence":[31,70],"critical":[34],"wave":[35,65],"number":[36,41],"kcrit":[37],"which":[38],"limits":[39],"hydrodynamic":[43,76,97],"modes":[44],"frequency":[47],"space.":[48],"This":[49],"implies":[50],"that":[51],"there":[52],"are":[53],"only":[54],"finitely":[55],"many":[56],"isolated":[57],"eigenvalues":[58],"above":[59],"essential":[61],"spectrum":[62],"at":[63],"each":[64],"number,":[66],"thus":[67],"showing":[68],"finite-dimensional,":[73],"well-separated":[74],"manifold":[77],"as":[78,89],"combination":[80],"invariant":[82],"eigenspaces.":[83],"The":[84],"obtained":[85],"results":[86],"can":[87],"serve":[88],"benchmark":[91],"validating":[93],"approximate":[94],"theories":[95],"closures":[98],"and":[99,102],"moment":[100],"methods":[101],"provides":[103],"basis":[105],"closure":[109],"operator.":[110]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}