{"id":"https://openalex.org/W1611229675","doi":"https://doi.org/10.1137/060660552","title":"On the Well-Posedness for the Viscous Shallow Water Equations","display_name":"On the Well-Posedness for the Viscous Shallow Water Equations","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1611229675","doi":"https://doi.org/10.1137/060660552","mag":"1611229675"},"language":"en","primary_location":{"id":"doi:10.1137/060660552","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060660552","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/math/0606081","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Qionglei Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qionglei Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Changxing Miao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Changxing Miao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Zhifei Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhifei Zhang","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":2.0358,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.83643182,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"40","issue":"2","first_page":"443","last_page":"474"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9854999780654907,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9854999780654907,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.006000000052154064,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.0032999999821186066,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7684999704360962},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6935999989509583},{"id":"https://openalex.org/keywords/shallow-water-equations","display_name":"Shallow water equations","score":0.6585000157356262},{"id":"https://openalex.org/keywords/waves-and-shallow-water","display_name":"Waves and shallow water","score":0.5529999732971191},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.33410000801086426},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.32710000872612}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7879999876022339},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7684999704360962},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6935999989509583},{"id":"https://openalex.org/C140295346","wikidata":"https://www.wikidata.org/wiki/Q4008384","display_name":"Shallow water equations","level":2,"score":0.6585000157356262},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6266000270843506},{"id":"https://openalex.org/C186348155","wikidata":"https://www.wikidata.org/wiki/Q7975538","display_name":"Waves and shallow water","level":2,"score":0.5529999732971191},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.33410000801086426},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.32710000872612},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.3010999858379364},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C182692853","wikidata":"https://www.wikidata.org/wiki/Q2386647","display_name":"Primitive equations","level":4,"score":0.26910001039505005},{"id":"https://openalex.org/C71351571","wikidata":"https://www.wikidata.org/wiki/Q7935890","display_name":"Viscous liquid","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.2644999921321869}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/060660552","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060660552","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/0606081","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0606081","pdf_url":"https://arxiv.org/pdf/math/0606081","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:math/0606081","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0606081","pdf_url":"https://arxiv.org/pdf/math/0606081","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1489373617","https://openalex.org/W1969615700","https://openalex.org/W1977063808","https://openalex.org/W1985898993","https://openalex.org/W1998016971","https://openalex.org/W2012791294","https://openalex.org/W2018233425","https://openalex.org/W2039350114","https://openalex.org/W2043876702","https://openalex.org/W2048990560","https://openalex.org/W2064433243","https://openalex.org/W2072280393","https://openalex.org/W2074329966","https://openalex.org/W2086473339","https://openalex.org/W2331086669","https://openalex.org/W2383986130"],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"prove":[4],"the":[5,10,13,24,30],"existence":[6],"and":[7],"uniqueness":[8],"of":[9],"solutions":[11],"for":[12],"two-dimensional":[14],"viscous":[15],"shallow":[16],"water":[17],"equations":[18],"with":[19],"low":[20],"regularity":[21],"assumptions":[22],"on":[23],"initial":[25,31],"data":[26],"as":[27,29],"well":[28],"height":[32],"bounded":[33],"away":[34],"from":[35],"zero.":[36]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2016-06-24T00:00:00"}