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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":"-1 1","pages":""},"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":"-1 1","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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":"-1 1","pages":""},"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
An optimal support function related to the strong openness conjecture 与强开放猜想相关的最优支持函数
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-05-17 DOI: 10.2969/jmsj/87048704
Q. Guan, Zheng Yuan
{"title":"An optimal support function related to the strong openness conjecture","authors":"Q. Guan, Zheng Yuan","doi":"10.2969/jmsj/87048704","DOIUrl":"https://doi.org/10.2969/jmsj/87048704","url":null,"abstract":". In the present article, we obtain an optimal support function of weighted L 2 integrations on superlevel sets of psh weights, which implies the strong openness property of multiplier ideal sheaves.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45225667","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
Large deviations for values of $L$-functions attached to cusp forms in the level aspect 在水平方面，附属于尖端形式的$L$函数值的较大偏差
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-05-12 DOI: 10.2969/jmsj/88888888
Masahiro Mine
{"title":"Large deviations for values of $L$-functions attached to cusp forms in the level aspect","authors":"Masahiro Mine","doi":"10.2969/jmsj/88888888","DOIUrl":"https://doi.org/10.2969/jmsj/88888888","url":null,"abstract":"We study the distribution of values of automorphic L-functions in a family of holomorphic cusp forms with prime level. We prove an asymptotic formula for a certain density function closely related to this value-distribution. The formula is applied to estimate large values of L-functions.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42146861","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
Localization formulas of cohomology intersection numbers 上同调交数的局部化公式
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-04-26 DOI: 10.2969/jmsj/87738773
Saiei-Jaeyeong Matsubara-Heo
{"title":"Localization formulas of cohomology intersection numbers","authors":"Saiei-Jaeyeong Matsubara-Heo","doi":"10.2969/jmsj/87738773","DOIUrl":"https://doi.org/10.2969/jmsj/87738773","url":null,"abstract":"We revisit the localization formulas of cohomology intersection numbers associated to a logarithmic connection. The main contribution of this paper is threefold: we prove the localization formula of the cohomology intersection number of logarithmic forms in terms of residue of a connection; we prove that the leading term of the Laurent expansion of the cohomology intersection number is Grothendieck residue when the connection is hypergeometric; and we prove that the leading term of stringy integral discussed by Arkani-Hamed, He and Lam is nothing but the self-cohomology intersection number of the canonical form.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49506370","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
On the positivity of the dimension of the global sections of adjoint bundle for quasi-polarized manifold with numerically trivial canonical bundle 具有数值平凡正则束的拟极化流形伴随束整体截面维数的正性
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2021-04-13 DOI: 10.2969/JMSJ/84588458
Y. Fukuma
{"title":"On the positivity of the dimension of the global sections of\u0000 adjoint bundle for quasi-polarized manifold with numerically trivial canonical bundle","authors":"Y. Fukuma","doi":"10.2969/JMSJ/84588458","DOIUrl":"https://doi.org/10.2969/JMSJ/84588458","url":null,"abstract":"Let (X, L) denote a quasi-polarized manifold of dimension n ≥ 5 defined over the field of complex numbers such that the canonical line bundle KX of X is numerically equivalent to zero. In this paper, we consider the dimension of the global sections of KX + mL in this case, and we prove that h(KX + mL) > 0 for every positive integer m with m ≥ n − 3. In particular, a Beltrametti-Sommese conjecture is true for quasi-polarized manifolds with numerically trivial canonical divisors.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43339968","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
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