{"title":"Rationality and fusion rules of exceptional $mathcal {W}$-algebras","authors":"T. Arakawa, Jethro van Ekeren","doi":"10.4171/jems/1250","DOIUrl":"https://doi.org/10.4171/jems/1250","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"34 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90177963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Proper base change for étale sheaves of spaces","authors":"Chang-Yeon Chough","doi":"10.4171/jems/1263","DOIUrl":"https://doi.org/10.4171/jems/1263","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"63 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85511457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Erratum to “Uniform boundary controllability and homogenization of wave equations”","authors":"F. Lin, Zhongwei Shen","doi":"10.4171/jems/1261","DOIUrl":"https://doi.org/10.4171/jems/1261","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"20 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80950175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Effective joint equidistribution of primitive rational points on expanding horospheres","authors":"Daniel El-Baz,Bingrong Huang,Min Lee","doi":"10.4171/jems/1238","DOIUrl":"https://doi.org/10.4171/jems/1238","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"1 6","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Commensurated subgroups and micro-supported actions (with an appendix by Dominik Francoeur)","authors":"P. Caprace, Adrien Le Boudec","doi":"10.4171/jems/1236","DOIUrl":"https://doi.org/10.4171/jems/1236","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"114 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79249149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stationary $C^*$-dynamical systems (with an appendix by Uri Bader, Yair Hartman, and Mehrdad Kalantar)","authors":"Yair Hartman, Mehrdad Kalantar","doi":"10.4171/jems/1225","DOIUrl":"https://doi.org/10.4171/jems/1225","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"27 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89832133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Riemannian quantitative isoperimetric inequality","authors":"Otis Chodosh,Max Engelstein,Luca Spolaor","doi":"10.4171/jems/1223","DOIUrl":"https://doi.org/10.4171/jems/1223","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"2 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Integral $p$-adic Hodge filtrations in low dimension and ramification","authors":"Shizhang Li","doi":"10.4171/jems/1237","DOIUrl":"https://doi.org/10.4171/jems/1237","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"3 4","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Instabilities of invariant quasi-periodic tori","authors":"Gerard Farré,Bassam Fayad","doi":"10.4171/jems/1206","DOIUrl":"https://doi.org/10.4171/jems/1206","url":null,"abstract":"","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"4 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In a smoothly bounded convex domain Ω ⊂ R, we consider the chemotaxis-Navier-Stokes model nt + u · ∇n = ∆n−∇ · (n∇c), x ∈ Ω, t > 0, ct + u · ∇c = ∆c− nc, x ∈ Ω, t > 0, ut + (u · ∇)u = ∆u+∇P + n∇Φ, ∇ · u = 0, x ∈ Ω, t > 0, (⋆) proposed by Goldstein et al. to describe pattern formation in populations of aerobic bacteria interacting with their liquid environment via transport and buoyancy. Known results have asserted that under appropriate regularity assumptions on Φ and the initial data, a corresponding no-flux/noflux/Dirichlet initial-boundary value problem is globally solvable in a framework of so-called weak energy solutions, and that any such solution eventually becomes smooth and classical. Going beyond this, the present work focuses on the possible extent of unboundedness phenomena also on short timescales, and hence investigates in more detail the set of times in (0,∞) at which solutions may develop singularities. The main results in this direction reveal the existence of a global weak energy solution which coincides with a smooth function throughout Ω × E, where E denotes a countable union of open intervals which is such that |(0,∞) E| = 0. In particular, this indicates that a similar feature of the unperturbed Navier-Stokes equations, known as Leray’s structure theorem, persists even in the presence of the coupling to the attractive and hence potentially destabilizing cross-diffusive mechanism in the full system (⋆).
{"title":"Does Leray’s structure theorem withstand buoyancy-driven chemotaxis-fluid interaction?","authors":"M. Winkler","doi":"10.4171/jems/1226","DOIUrl":"https://doi.org/10.4171/jems/1226","url":null,"abstract":"In a smoothly bounded convex domain Ω ⊂ R, we consider the chemotaxis-Navier-Stokes model nt + u · ∇n = ∆n−∇ · (n∇c), x ∈ Ω, t > 0, ct + u · ∇c = ∆c− nc, x ∈ Ω, t > 0, ut + (u · ∇)u = ∆u+∇P + n∇Φ, ∇ · u = 0, x ∈ Ω, t > 0, (⋆) proposed by Goldstein et al. to describe pattern formation in populations of aerobic bacteria interacting with their liquid environment via transport and buoyancy. Known results have asserted that under appropriate regularity assumptions on Φ and the initial data, a corresponding no-flux/noflux/Dirichlet initial-boundary value problem is globally solvable in a framework of so-called weak energy solutions, and that any such solution eventually becomes smooth and classical. Going beyond this, the present work focuses on the possible extent of unboundedness phenomena also on short timescales, and hence investigates in more detail the set of times in (0,∞) at which solutions may develop singularities. The main results in this direction reveal the existence of a global weak energy solution which coincides with a smooth function throughout Ω × E, where E denotes a countable union of open intervals which is such that |(0,∞) E| = 0. In particular, this indicates that a similar feature of the unperturbed Navier-Stokes equations, known as Leray’s structure theorem, persists even in the presence of the coupling to the attractive and hence potentially destabilizing cross-diffusive mechanism in the full system (⋆).","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"42 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2022-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84934888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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