{"id":"https://openalex.org/W2188597116","doi":"https://doi.org/10.1007/978-3-642-31034-8_16","title":"Applications of Integral Relations and Conservation Laws in the Theory of Hydrodynamic Stability","display_name":"Applications of Integral Relations and Conservation Laws in the Theory of Hydrodynamic Stability","publication_year":2012,"publication_date":"2012-10-25","ids":{"openalex":"https://openalex.org/W2188597116","doi":"https://doi.org/10.1007/978-3-642-31034-8_16","mag":"2188597116"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-31034-8_16","doi":"https://doi.org/10.1007/978-3-642-31034-8_16","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-31034-8_16","pdf_url":null,"source":{"id":"https://openalex.org/S4210171045","display_name":"Encyclopaedia of mathematical sciences","issn_l":"0938-0396","issn":["0938-0396","2512-3459"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Encyclopaedia of Mathematical Sciences","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W2503685833","display_name":"Fundamentals of Geophysical Hydrodynamics"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035081582","display_name":"Felix V. Dolzhansky","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Felix V. Dolzhansky","raw_affiliation_strings":["http://www.springer.com"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"http://www.springer.com","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5035081582"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.25917637,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"141","last_page":"150"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.8485999703407288,"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"}},"topics":[{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.8485999703407288,"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/T10255","display_name":"Oceanographic and Atmospheric Processes","score":0.11389999836683273,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.012600000016391277,"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/hydrodynamic-stability","display_name":"hydrodynamic stability","score":0.9890000224113464},{"id":"https://openalex.org/keywords/fluid-stratification","display_name":"stratified fluid","score":0.9559999704360962},{"id":"https://openalex.org/keywords/richardson-number","display_name":"Richardson number","score":0.9229999780654907},{"id":"https://openalex.org/keywords/plane-parallel-flow","display_name":"plane-parallel flow","score":0.8050000071525574},{"id":"https://openalex.org/keywords/quadratic-forms","display_name":"quadratic forms","score":0.5009999871253967},{"id":"https://openalex.org/keywords/eigenvalue-spectrum","display_name":"eigenvalue spectrum","score":0.7200000286102295},{"id":"https://openalex.org/keywords/conservation-laws","display_name":"conservation laws","score":0.6729999780654907},{"id":"https://openalex.org/keywords/integral-relations","display_name":"integral relations","score":0.6800000071525574},{"id":"https://openalex.org/keywords/linear-stability-analysis","display_name":"linear stability analysis","score":0.675000011920929}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.653950035572052},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6169754862785339},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5900746583938599},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.47917261719703674},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.4740980565547943},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4594931900501251},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.44411763548851013},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.43946847319602966},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43080925941467285},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.4216955602169037},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.40974104404449463},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3886207342147827},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34812620282173157},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3361744284629822},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23748177289962769},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1626562476158142},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13360241055488586},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0845552384853363},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-31034-8_16","doi":"https://doi.org/10.1007/978-3-642-31034-8_16","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-31034-8_16","pdf_url":null,"source":{"id":"https://openalex.org/S4210171045","display_name":"Encyclopaedia of mathematical sciences","issn_l":"0938-0396","issn":["0938-0396","2512-3459"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Encyclopaedia of Mathematical Sciences","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W2016206105","https://openalex.org/W2070342944","https://openalex.org/W2166042724"],"related_works":["https://openalex.org/W2070342944","https://openalex.org/W2014605738","https://openalex.org/W2318148106","https://openalex.org/W4383382977","https://openalex.org/W1785189794","https://openalex.org/W3195465533","https://openalex.org/W3119869742","https://openalex.org/W2161728489","https://openalex.org/W2887130952","https://openalex.org/W2083264445"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-10-10T09:11:00.788812","created_date":"2016-06-24T00:00:00"}