{"id":"https://openalex.org/W7212111448","doi":"https://doi.org/10.48550/arxiv.2609.09900","title":"On the rotation-two-component $b$-family shallow-water system: derivation and wave-breaking analysis","display_name":"On the rotation-two-component $b$-family shallow-water system: derivation and wave-breaking analysis","publication_year":2026,"publication_date":"2026-09-09","ids":{"openalex":"https://openalex.org/W7212111448","doi":"https://doi.org/10.48550/arxiv.2609.09900"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.09900","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09900","pdf_url":"https://arxiv.org/pdf/2609.09900","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.09900","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151125595","display_name":"Xingxing Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Liu, Xingxing","raw_affiliation_strings":["Jiangsu Center for Applied Mathematics (CUMT) , Xuzhou , Jiangsu 221116 , China","School of Mathematics , China University of Mining and Technology , Xuzhou , Jiangsu 221116 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jiangsu Center for Applied Mathematics (CUMT) , Xuzhou , Jiangsu 221116 , China","institution_ids":["https://openalex.org/I25757504"]},{"raw_affiliation_string":"School of Mathematics , China University of Mining and Technology , Xuzhou , Jiangsu 221116 , China","institution_ids":["https://openalex.org/I25757504"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5151125595"],"corresponding_institution_ids":["https://openalex.org/I25757504"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9229000210762024,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9229000210762024,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.07079999893903732,"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"}},{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.0010000000474974513,"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/shallow-water-waves","display_name":"shallow water waves","score":0.8259999752044678},{"id":"https://openalex.org/keywords/green-naghdi-equations","display_name":"Green-Naghdi equations","score":0.9380000233650208},{"id":"https://openalex.org/keywords/coriolis-force","display_name":"Coriolis force","score":0.9929999709129333},{"id":"https://openalex.org/keywords/constant-vorticity","display_name":"constant vorticity","score":0.9509999752044678},{"id":"https://openalex.org/keywords/two-component-camassa-holm-system","display_name":"two-component Camassa-Holm system","score":0.8230000138282776},{"id":"https://openalex.org/keywords/wave-breaking","display_name":"wave breaking","score":0.8679999709129333},{"id":"https://openalex.org/keywords/blow-up-criterion","display_name":"blow-up criterion","score":0.9919999837875366},{"id":"https://openalex.org/keywords/auxiliary-variables","display_name":"auxiliary variables","score":0.7580000162124634}],"concepts":[{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5697000026702881},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5690000057220459},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.5388000011444092},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5192999839782715},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5062000155448914},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.47269999980926514},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.4603999853134155},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.44620001316070557},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41290000081062317},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.40720000863075256},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.38190001249313354},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.33550000190734863},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.3310000002384186},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.32409998774528503},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.29109999537467957},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C5555538","wikidata":"https://www.wikidata.org/wiki/Q6823703","display_name":"Method of averaging","level":3,"score":0.28690001368522644},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2854999899864197},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.28439998626708984},{"id":"https://openalex.org/C183276030","wikidata":"https://www.wikidata.org/wiki/Q1193095","display_name":"Coupling constant","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C171912257","wikidata":"https://www.wikidata.org/wiki/Q11019","display_name":"Mechanical system","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2700999975204468},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2597000002861023},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.257099986076355}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.09900","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09900","pdf_url":"https://arxiv.org/pdf/2609.09900","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,"listed_in":[],"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"},{"id":"doi:10.48550/arxiv.2609.09900","doi":"https://doi.org/10.48550/arxiv.2609.09900","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.09900","pdf_url":null,"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,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.09900","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09900","pdf_url":"https://arxiv.org/pdf/2609.09900","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,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4695639219","display_name":null,"funder_award_id":"12001528","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212111448.pdf","grobid_xml":"https://content.openalex.org/works/W7212111448.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3003628603","https://openalex.org/W4400735448","https://openalex.org/W7117718456","https://openalex.org/W2234746416","https://openalex.org/W1852677413","https://openalex.org/W2982082993","https://openalex.org/W2086295598","https://openalex.org/W4300893984","https://openalex.org/W4406066236","https://openalex.org/W2029257378"],"abstract_inverted_index":{"In":[0],"this":[1,114],"paper,":[2],"we":[3,117,137],"derive":[4,138],"the":[5,12,17,20,33,51,60,69,80,96,109,144,154,164,175,184],"rotation-two-component":[6,61],"$b$-family":[7,186],"shallow-water":[8],"wave":[9],"system":[10,27,37,156,166],"from":[11],"Green--Naghdi":[13],"type":[14,83],"equations":[15],"incorporating":[16],"effects":[18],"of":[19,50,77,183],"Coriolis":[21,110,145],"force":[22,146],"and":[23,92,122,157,167,178],"constant":[24],"vorticity.":[25],"The":[26,170],"admits,":[28],"among":[29],"its":[30,43],"special":[31,181],"cases,":[32],"two-component":[34,81],"Degasperis--Procesi":[35],"(2DP)":[36],"as":[38,46],"a":[39,47,57,102,124],"reduction,":[40,59],"thereby":[41],"confirming":[42],"genuine":[44],"role":[45],"rotational":[48,185],"extension":[49],"$b$-family.":[52],"We":[53],"then":[54],"focus":[55],"on":[56,135],"specific":[58],"Degasperis-Procesi":[62,168],"system,":[63,84,99],"whose":[64],"particular":[65],"interest":[66],"lies":[67],"in":[68,93],"fact":[70],"that":[71],"it":[72,85,100],"combines":[73],"two":[74,139],"independent":[75],"sources":[76],"difficulty:":[78],"unlike":[79],"Camassa-Holm":[82],"possesses":[86],"no":[87],"conserved":[88],"$H^1\\times":[89],"L^2$-type":[90],"quantity,":[91],"contrast":[94],"to":[95,174,179],"standard":[97],"2DP":[98,155,165],"contains":[101],"higher-order":[103],"nonlinear":[104],"coupling":[105],"term":[106],"induced":[107],"by":[108],"force.":[111],"To":[112],"overcome":[113],"double":[115],"difficulty,":[116],"introduce":[118],"an":[119],"auxiliary":[120],"variable":[121],"establish":[123],"local":[125],"$L^\\infty$-estimate":[126],"for":[127,153,162],"$u$":[128],"without":[129],"using":[130],"any":[131],"conservation":[132],"law,":[133],"based":[134],"which":[136],"distinct":[140],"blow-up":[141],"criteria.":[142],"When":[143],"vanishes,":[147],"our":[148],"results":[149,171],"recover":[150],"known":[151],"criteria":[152,161],"also":[158],"provide":[159],"new":[160],"both":[163],"equation.":[169],"extend":[172],"naturally":[173],"periodic":[176],"setting":[177],"relevant":[180],"cases":[182],"system.":[187]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-11T00:00:00"}