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On global existence for semilinear wave equations with space-dependent critical damping 具有空间相关临界阻尼的双线性波动方程的全局存在性
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-06-11 DOI: 10.2969/jmsj/87388738
M. Sobajima
{"title":"On global existence for semilinear wave equations with space-dependent critical damping","authors":"M. Sobajima","doi":"10.2969/jmsj/87388738","DOIUrl":"https://doi.org/10.2969/jmsj/87388738","url":null,"abstract":"The global existence for semilinear wave equations with space-dependent critical damping ∂ t u−∆u+ V0 |x| ∂tu = f(u) in an exterior domain is dealt with, where f(u) = |u|p−1u and f(u) = |u| are in mind. Existence and non-existence of global-in-time solutions are discussed. To obtain global existence, a weighted energy estimate for the linear problem is crucial. The proof of such a weighted energy estimate contains an alternative proof of energy estimates established by Ikehata–Todorova–Yordanov [J. Math. Soc. Japan (2013), 183–236] but this clarifies the precise independence of the location of the support of initial data. The blowup phenomena is verified by using a test function method with positive harmonic functions satisfying the Dirichlet boundary condition. Mathematics Subject Classification (2010): Primary:35L71, 35A01, Secondary:35L20, 35B40,","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41972379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A virtual knot whose virtual unknotting number equals one and a sequence of $n$-writhes 一种虚拟结，其虚拟解结数等于1，并有一个$n$-缠绕的序列
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-06-04 DOI: 10.2969/JMSJ/84478447
Y. Ohyama, Migiwa Sakurai
{"title":"A virtual knot whose virtual unknotting number equals one and a sequence of $n$-writhes","authors":"Y. Ohyama, Migiwa Sakurai","doi":"10.2969/JMSJ/84478447","DOIUrl":"https://doi.org/10.2969/JMSJ/84478447","url":null,"abstract":"Satoh and Taniguchi introduced the n-writhe Jn for each non-zero integer n, which is an integer invariant for virtual knots. The sequence of n-writhes {Jn}n̸=0 of a virtual knot K satisfies ∑ n̸=0 nJn(K) = 0. They showed that for any sequence of integers {cn}n̸=0 with ∑ n̸=0 ncn = 0, there exists a virtual knot K with Jn(K) = cn for any n ̸= 0. It is obvious that the virtualization of a real crossing is an unknotting operation for virtual knots. The unknotting number by the virtualization is called the virtual unknotting number and is denoted by uv . In this paper, we show that if {cn}n̸=0 is a sequence of integers with ∑ n̸=0 ncn = 0, then there exists a virtual knot K such that uv(K) = 1 and Jn(K) = cn for any n ̸= 0.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44270488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Estimates of the renewal measure 更新措施的估计
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-06-04 DOI: 10.2969/JMSJ/83298329
H. Carlsson
{"title":"Estimates of the renewal measure","authors":"H. Carlsson","doi":"10.2969/JMSJ/83298329","DOIUrl":"https://doi.org/10.2969/JMSJ/83298329","url":null,"abstract":"We prove sharp estimates for the renewal measure of a strongly nonlattice probability measure on the real line. In particular we consider the case where the measure has finite moments between 1 and 2. The proof uses Fourier analysis of tempered distributions.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49098759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bridgeland stability of minimal instanton bundles on Fano threefolds Fano上最小瞬时束的桥地稳定性
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-05-30 DOI: 10.2969/jmsj/89238923
Xuqiang Qin
{"title":"Bridgeland stability of minimal instanton bundles on Fano threefolds","authors":"Xuqiang Qin","doi":"10.2969/jmsj/89238923","DOIUrl":"https://doi.org/10.2969/jmsj/89238923","url":null,"abstract":"We prove that minimal instanton bundles on a Fano threefold $X$ of Picard rank one and index two are semistable objects in the Kuznetsov component $mathsf{Ku}(X)$, with respect to the stability conditions constructed by Bayer, Lahoz, Macr`i and Stellari. When the degree of $X$ is at least $3$, we show torsion free generalizations of minimal instantons are also semistable objects. As a result, we describe the moduli space of semistable objects with same numerical classes as minimal instantons in $mathsf{Ku}(X)$. We also investigate the stability of acyclic extensions of non-minimal instantons.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43170506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Ill-posedness for the compressible Navier–Stokes equations under barotropic condition in limiting Besov spaces 限制Besov空间中正压条件下可压缩Navier-Stokes方程的病态性
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-05-26 DOI: 10.2969/JMSJ/81598159
T. Iwabuchi, T. Ogawa
{"title":"Ill-posedness for the compressible Navier–Stokes equations under barotropic condition in limiting Besov spaces","authors":"T. Iwabuchi, T. Ogawa","doi":"10.2969/JMSJ/81598159","DOIUrl":"https://doi.org/10.2969/JMSJ/81598159","url":null,"abstract":"We consider the compressible Navier–Stokes system in the critical Besov spaces. It is known that the system is (semi-)well-posed in the scaling semi-invariant spaces of the homogeneous Besov spaces Ḃ n p p,1 × Ḃ n p −1 p,1 for all 1 ≤ p < 2n. However, if the data is in a larger scaling invariant class such as p > 2n, then the system is not well-posed. In this paper, we demonstrate that for the critical case p = 2n the system is ill-posed by showing that a sequence of initial data is constructed to show discontinuity of the solution map in the critical space. Our result indicates that the well-posedness results due to Danchin [10] and Haspot [18] are indeed sharp in the framework of the homogeneous Besov spaces.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69574279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Functional calculus of Laplace transform type on non-doubling parabolic manifolds with ends 带端非倍抛物流形拉普拉斯变换型的泛函演算
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-05-26 DOI: 10.2969/JMSJ/83348334
Hong Chuong Doan
{"title":"Functional calculus of Laplace transform type on non-doubling parabolic manifolds with ends","authors":"Hong Chuong Doan","doi":"10.2969/JMSJ/83348334","DOIUrl":"https://doi.org/10.2969/JMSJ/83348334","url":null,"abstract":"Let M be a non-doubling parabolic manifold with ends and L a non-negative self-adjoint operator on L2(M) which satisfies a suitable heat kernel upper bound named the upper bound of Gaussian type. These operators include the Schrödinger operators L = ∆ + V where ∆ is the Laplace-Beltrami operator and V is an arbitrary non-negative potential. This paper will investigate the behaviour of the Poisson semi-group kernels of L together with its time derivatives and then apply them to obtain the weak type (1, 1) estimate of the functional calculus of Laplace transform type of √ L which is defined by M( √ L)f(x) := ́∞ 0 [√ Le−t √ Lf(x) ] m(t)dt where m(t) is a bounded function on [0,∞). In the setting of our study, both doubling condition of the measure on M and the smoothness of the operators’ kernels are missing. The purely imaginary power Lis, s ∈ R, is a special case of our result and an example of weak type (1, 1) estimates of a singular integral with non-smooth kernels on non-doubling spaces.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69574353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deformation for coupled Kähler–Einstein metrics 耦合Kähler–Einstein度量的形变
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-05-26 DOI: 10.2969/JMSJ/84408440
Satoshi X. Nakamura
{"title":"Deformation for coupled Kähler–Einstein metrics","authors":"Satoshi X. Nakamura","doi":"10.2969/JMSJ/84408440","DOIUrl":"https://doi.org/10.2969/JMSJ/84408440","url":null,"abstract":"The notion of coupled Kähler-Einstein metrics was introduced recently by Hultgren-WittNyström. In this paper we discuss deformation of a coupled KählerEinstein metric on a Fano manifold. We obtain a necessary and sufficient condition for a coupled Kähler-Einstein metric to be deformed to another coupled Kähler-Einstein metric for a Fano manifold admitting non-trivial holomorphic vector fields. In addition we also discuss deformation for a coupled Käher-Einstein metric on a Fano manifold when the complex structure varies.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47300822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Torsion of algebraic groups and iterate extensions associated with Lubin–Tate formal groups 与Lubin-Tate形式群相关的代数群的扭转和迭代扩展
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-05-24 DOI: 10.2969/jmsj/87238723
Yoshiyasu Ozeki
{"title":"Torsion of algebraic groups and iterate extensions associated with Lubin–Tate formal groups","authors":"Yoshiyasu Ozeki","doi":"10.2969/jmsj/87238723","DOIUrl":"https://doi.org/10.2969/jmsj/87238723","url":null,"abstract":"We show finiteness results on torsion points of commutative algebraic groups over a p-adic field K with values in various algebraic extensions L/K of infinite degree. We mainly study the following cases: (1) L is an abelian extension which is a splitting field of a crystalline character (such as a Lubin-Tate extension). (2) L is a certain iterate extension of K associated with Lubin-Tate formal groups, which is familiar with Kummer theory.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43446645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ohno relation for regularized multiple zeta values 正则化多个zeta值的Ohno关系
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-05-20 DOI: 10.2969/jmsj/89088908
M. Hirose, H. Murahara, Shingo Saito
{"title":"Ohno relation for regularized multiple zeta values","authors":"M. Hirose, H. Murahara, Shingo Saito","doi":"10.2969/jmsj/89088908","DOIUrl":"https://doi.org/10.2969/jmsj/89088908","url":null,"abstract":"The Ohno relation for multiple zeta values can be formulated as saying that a certain operator, defined for indices, is invariant under taking duals. In this paper, we generalize the Ohno relation to regularized multiple zeta values by showing that, although the suitably generalized operator is not invariant under taking duals, the relation between its values at an index and at its dual index can be written explicitly in terms of the gamma function.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47935591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Homogenization of symmetric Dirichlet forms 对称Dirichlet形式的均匀化
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-05-18 DOI: 10.2969/JMSJ/85268526
M. Tomisaki, T. Uemura
{"title":"Homogenization of symmetric Dirichlet forms","authors":"M. Tomisaki, T. Uemura","doi":"10.2969/JMSJ/85268526","DOIUrl":"https://doi.org/10.2969/JMSJ/85268526","url":null,"abstract":"We consider a homogenization problem for symmetric jumpdiffusion processes by using the Mosco convergence and the two-scale convergence of the corresponding Dirichlet forms. Moreover, we show the weak convergence of the processes.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41317674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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