{"title":"On the Lagrangian Description and Uniqueness for the one-dimensional Pressureless Euler System","authors":"Mark D. Suder","doi":"10.33915/etd.10184","DOIUrl":"https://doi.org/10.33915/etd.10184","url":null,"abstract":"","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69556339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Brakke's formulation of velocity and the second order regularity property","authors":"Ryunosuke Mori, Eita Tomimatsu, Yoshihiro Tonegawa","doi":"10.1512/iumj.2023.72.9558","DOIUrl":"https://doi.org/10.1512/iumj.2023.72.9558","url":null,"abstract":"","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135503390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1512/iumj.2023.72.9488
Adachi Masanori, Masanori Adachi
We prove the following result that was conjectured by Brunella: Let $X$ be a compact complex manifold of dimension $geq 3$. Let $mathcal{F}$ be a codimension one holomorphic foliation on $X$ with ample normal bundle. Then every leaf of $mathcal{F}$ accumulates to the singular set of $mathcal{F}$.
{"title":"Dynamical aspects of foliations with ample normal bundle","authors":"Adachi Masanori, Masanori Adachi","doi":"10.1512/iumj.2023.72.9488","DOIUrl":"https://doi.org/10.1512/iumj.2023.72.9488","url":null,"abstract":"We prove the following result that was conjectured by Brunella: Let $X$ be a compact complex manifold of dimension $geq 3$. Let $mathcal{F}$ be a codimension one holomorphic foliation on $X$ with ample normal bundle. Then every leaf of $mathcal{F}$ accumulates to the singular set of $mathcal{F}$.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135503404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1512/iumj.2023.72.9135
Ming Wang, Ze Li, Shanlin Huang
{"title":"Unique continuation inequalities for nonlinear Schroedinger equations based on uncertainty principles","authors":"Ming Wang, Ze Li, Shanlin Huang","doi":"10.1512/iumj.2023.72.9135","DOIUrl":"https://doi.org/10.1512/iumj.2023.72.9135","url":null,"abstract":"","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66765962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1512/iumj.2023.72.9544
Christoph Walker
{"title":"Properties of the semigroup in L_1 associated with age-structured diffusive properties","authors":"Christoph Walker","doi":"10.1512/iumj.2023.72.9544","DOIUrl":"https://doi.org/10.1512/iumj.2023.72.9544","url":null,"abstract":"","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135503134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-15DOI: 10.1512/iumj.2022.71.9091
Razvan-Octavian Radu
. In [3], Bertozzi and Constantin formulate the vortex patch problem in the level-set framework and prove a priori estimates for this active scalar equation. By extending the tools used to prove these estimates, we construct solutions and show propagation of higher H¨older regularity. This constitutes a proof of the regularity of vortex patches, carried out solely in the level-set framework.
{"title":"Existence and regularity for vortex patch solutions of the 2D Euler equations","authors":"Razvan-Octavian Radu","doi":"10.1512/iumj.2022.71.9091","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.9091","url":null,"abstract":". In [3], Bertozzi and Constantin formulate the vortex patch problem in the level-set framework and prove a priori estimates for this active scalar equation. By extending the tools used to prove these estimates, we construct solutions and show propagation of higher H¨older regularity. This constitutes a proof of the regularity of vortex patches, carried out solely in the level-set framework.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46814172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-21DOI: 10.1512/iumj.2023.72.9323
Huaying Wei, Katsuhiko Matsuzaki
We investigate strongly symmetric homeomorphisms of the real line which appear in harmonic analysis aspects of quasiconformal Teichm"uller theory. An element in this class can be characterized by a property that it can be extended quasiconformally to the upper half-plane so that its complex dilatation induces a vanishing Carleson measure. However, differently from the case on the unit circle, strongly symmetric homeomorphisms on the real line are not preserved under either the composition or the inversion. In this paper, we present the difference and the relation between these two cases. In particular, we show that if uniform continuity is assumed for strongly symmetric homeomorphisms of the real line, then they are preserved by those operations. We also show that the barycentric extension of uniformly continuous one induces a vanishing Carleson measure and so do the composition and the inverse of those quasiconformal homeomorphisms of the upper half-plane.
{"title":"Strongly symmetric homeomorphisms on the real line with uniform continuity","authors":"Huaying Wei, Katsuhiko Matsuzaki","doi":"10.1512/iumj.2023.72.9323","DOIUrl":"https://doi.org/10.1512/iumj.2023.72.9323","url":null,"abstract":"We investigate strongly symmetric homeomorphisms of the real line which appear in harmonic analysis aspects of quasiconformal Teichm\"uller theory. An element in this class can be characterized by a property that it can be extended quasiconformally to the upper half-plane so that its complex dilatation induces a vanishing Carleson measure. However, differently from the case on the unit circle, strongly symmetric homeomorphisms on the real line are not preserved under either the composition or the inversion. In this paper, we present the difference and the relation between these two cases. In particular, we show that if uniform continuity is assumed for strongly symmetric homeomorphisms of the real line, then they are preserved by those operations. We also show that the barycentric extension of uniformly continuous one induces a vanishing Carleson measure and so do the composition and the inverse of those quasiconformal homeomorphisms of the upper half-plane.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48830997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-09DOI: 10.1512/iumj.2022.71.9196
Yuusuke Sugiyama
We consider the blow-up of solutions to the following parameterized nonlinear wave equation: utt = c(u)uxx + λc(u)c(u)(ux) with the real parameter λ. In previous works, it was reported that there exist finite time blow-up solutions with λ = 1 and 2. However, the construction of a blow-up solution depends on the symmetric structure of the equation (e.g., the energy conservation law). In the present paper, we extend the blow-up result with λ = 1 to the case with λ ∈ (0, 1] by using a new L2/λ estimate. Moreover, some properties for the blow-up solution including the Hölder continuity are also discussed.
{"title":"Formation of singularities for a family of 1D quasilinear wave equations","authors":"Yuusuke Sugiyama","doi":"10.1512/iumj.2022.71.9196","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.9196","url":null,"abstract":"We consider the blow-up of solutions to the following parameterized nonlinear wave equation: utt = c(u)uxx + λc(u)c(u)(ux) with the real parameter λ. In previous works, it was reported that there exist finite time blow-up solutions with λ = 1 and 2. However, the construction of a blow-up solution depends on the symmetric structure of the equation (e.g., the energy conservation law). In the present paper, we extend the blow-up result with λ = 1 to the case with λ ∈ (0, 1] by using a new L2/λ estimate. Moreover, some properties for the blow-up solution including the Hölder continuity are also discussed.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46302197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-09DOI: 10.1512/iumj.2023.72.9755
E. Humbert, Y. Privat, Emmanuel Tr'elat
We establish some properties of quantum limits on a product manifold, proving for instance that, under appropriate assumptions, the quantum limits on the product of manifolds are absolutely continuous if the quantum limits on each manifolds are absolutely continuous. On a product of Riemannian manifolds satisfying the minimal multiplicity property, we prove that a periodic geodesic can never be charged by a quantum limit.
{"title":"Quantum limits on product manifolds","authors":"E. Humbert, Y. Privat, Emmanuel Tr'elat","doi":"10.1512/iumj.2023.72.9755","DOIUrl":"https://doi.org/10.1512/iumj.2023.72.9755","url":null,"abstract":"We establish some properties of quantum limits on a product manifold, proving for instance that, under appropriate assumptions, the quantum limits on the product of manifolds are absolutely continuous if the quantum limits on each manifolds are absolutely continuous. On a product of Riemannian manifolds satisfying the minimal multiplicity property, we prove that a periodic geodesic can never be charged by a quantum limit.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46330198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-08DOI: 10.1512/iumj.2022.71.9818
G. Bianchi, R. Gardner, P. Gronchi
Two related questions are discussed. The first is when reflection symmetry in a finite set of $i$-dimensional subspaces, $iin {1,dots,n-1}$, implies full rotational symmetry, i.e., the closure of the group generated by the reflections equals $O(n)$. For $i=n-1$, this has essentially been solved by Burchard, Chambers, and Dranovski, but new results are obtained for $iin {1,dots,n-2}$. The second question, to which an essentially complete answer is given, is when (full) rotational symmetry with respect to a finite set of $i$-dimensional subspaces, $iin {1,dots,n-2}$, implies full rotational symmetry, i.e., the closure of the group generated by all the rotations about each of the subspaces equals $SO(n)$. The latter result also shows that a closed set in $mathbb{R}^n$ that is invariant under rotations about more than one axis must be a union of spheres with their centers at the origin.
{"title":"Full rotational symmetry from reflections or rotational symmetries in finitely many subspaces","authors":"G. Bianchi, R. Gardner, P. Gronchi","doi":"10.1512/iumj.2022.71.9818","DOIUrl":"https://doi.org/10.1512/iumj.2022.71.9818","url":null,"abstract":"Two related questions are discussed. The first is when reflection symmetry in a finite set of $i$-dimensional subspaces, $iin {1,dots,n-1}$, implies full rotational symmetry, i.e., the closure of the group generated by the reflections equals $O(n)$. For $i=n-1$, this has essentially been solved by Burchard, Chambers, and Dranovski, but new results are obtained for $iin {1,dots,n-2}$. The second question, to which an essentially complete answer is given, is when (full) rotational symmetry with respect to a finite set of $i$-dimensional subspaces, $iin {1,dots,n-2}$, implies full rotational symmetry, i.e., the closure of the group generated by all the rotations about each of the subspaces equals $SO(n)$. The latter result also shows that a closed set in $mathbb{R}^n$ that is invariant under rotations about more than one axis must be a union of spheres with their centers at the origin.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42108742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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