Mathematische Zeitschrift最新文献_第2页

$$L^1-$$ decay of higher-order norms of solutions to the Navier–Stokes equations in the upper-half space 纳维-斯托克斯方程上半空间解的高阶规范的 $L^1-$$ 衰减

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-08-20 DOI: 10.1007/s00209-024-03578-6

Pigong Han

{"title":"$$L^1-$$ decay of higher-order norms of solutions to the Navier–Stokes equations in the upper-half space","authors":"Pigong Han","doi":"10.1007/s00209-024-03578-6","DOIUrl":"https://doi.org/10.1007/s00209-024-03578-6","url":null,"abstract":"The aim of this article devotes to establishing the (L^1)-decay of cubic order spatial derivatives of solutions to the Navier–Stokes equations, which is a long-time challenging problem. To solve this problem, new tools have to be found to overcome these main difficulties: (L^1-L^1) estimate fails for the Stokes flow; the projection operator (P:,L^1(mathbb {R}^n_+)rightarrow L^1_sigma (mathbb {R}^n_+)) becomes unbounded; the steady Stokes’s estimates does not work any more in (L^1(mathbb {R}^n_+)). We first give the asymptotic behavior with weights of negative exponent for the Stokes flow and Navier–Stokes equations in (L^1(mathbb {R}^n_+)), and these are also independent of interest by themselves. Secondly, we decompose the convection term into two parts, and translate the unboundedness of projection operator into studying an (L^1)-estimate for an elliptic problem with homogeneous Neumann boundary conditions, which is established by using the weighted estimates of the Gaussian kernel’s convolution. Finally, a crucial new formula is given for the fundamental solution of the Laplace operator, which is employed for overcoming the strong singularity in studying the cubic order spatial derivatives in (L^1(mathbb {R}^n_+)).","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"119 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

On the Gromov hyperbolicity of the minimal metric 论最小公设的格罗莫夫双曲性

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-08-20 DOI: 10.1007/s00209-024-03581-x

Matteo Fiacchi

引用次数: 0

The singular Yoneda category and the stabilization functor 米田奇异范畴和稳定化函子

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-08-17 DOI: 10.1007/s00209-024-03577-7

Xiao-Wu Chen, Zhengfang Wang

引用次数: 0

Stability theory for the NLS equation on looping edge graphs 循环边缘图上 NLS 方程的稳定性理论

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-08-11 DOI: 10.1007/s00209-024-03565-x

Jaime Angulo Pava

引用次数: 0

Holomorphic maps acting as Kobayashi isometries on a family of geodesics 作为小林等距线作用于测地线族的全态映射

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-08-11 DOI: 10.1007/s00209-024-03569-7

Filippo Bracci, Łukasz Kosiński, Włodzimierz Zwonek

引用次数: 0

Filtration of cohomology via symmetric semisimplicial spaces 通过对称半简空间的同调过滤

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-08-06 DOI: 10.1007/s00209-024-03563-z

Oishee Banerjee

{"title":"Filtration of cohomology via symmetric semisimplicial spaces","authors":"Oishee Banerjee","doi":"10.1007/s00209-024-03563-z","DOIUrl":"https://doi.org/10.1007/s00209-024-03563-z","url":null,"abstract":"In the simplicial theory of hypercoverings we replace the indexing category (Delta ) by the symmetric simplicial category (Delta S) and study (a class of) (Delta _{textrm{inj}}S)-hypercoverings, which we call spaces admitting symmetric (semi)simplicial filtration—this special class happens to have a structure of a module over a graded commutative monoid of the form (textrm{Sym},M) for some space M. For (Delta S)-hypercoverings we construct a spectral sequence, somewhat like the Čech-to-derived category spectral sequence. The advantage of working with (Delta S) over (Delta ) is that various combinatorial complexities that come with working on (Delta ) are bypassed, giving simpler, unified proof of results like the computation of (in some cases, stable) singular cohomology (with (mathbb {Q}) coefficients) and étale cohomology (with (mathbb {Q}_{ell }) coefficients) of the moduli space of degree n maps (Crightarrow mathbb {P}^r) with C a smooth projective curve of genus g, of unordered configuration spaces, of the moduli space of smooth sections of a fixed (mathfrak {g}^r_d) that is m-very ample for some m etc. In the special case when a (Delta _{textrm{inj}}S)-object X admits a symmetric semisimplicial filtration by M, we relate these moduli spaces to a certain derived tensor.","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"19 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Rearrangements and the Monge–Ampère equations 重排和蒙日-安培方程

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-08-06 DOI: 10.1007/s00209-024-03557-x

Zbigniew Błocki

引用次数: 0

Reduction by stages for finite W-algebras 有限 W 矩阵的逐级分解

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-08-03 DOI: 10.1007/s00209-024-03567-9

Naoki Genra, Thibault Juillard

引用次数: 0

Coderived and contraderived categories of locally presentable abelian DG-categories 局部可呈现阿贝尔DG类的编码类和反编码类

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-08-03 DOI: 10.1007/s00209-024-03519-3

Leonid Positselski, Jan Št’ovíček

{"title":"Coderived and contraderived categories of locally presentable abelian DG-categories","authors":"Leonid Positselski, Jan Št’ovíček","doi":"10.1007/s00209-024-03519-3","DOIUrl":"https://doi.org/10.1007/s00209-024-03519-3","url":null,"abstract":"The concept of an abelian DG-category, introduced by the first-named author in Positselski (Exact DG-categories and fully faithful triangulated inclusion functors. arXiv:2110.08237 [math.CT]), unites the notions of abelian categories and (curved) DG-modules in a common framework. In this paper we consider coderived and contraderived categories in the sense of Becker. Generalizing some constructions and results from the preceding papers by Becker (Adv Math 254:187–232, 2014. arXiv:1205.4473 [math.CT]) and by the present authors (Positselski and Št’ovíček in J Pure Appl Algebra 226(#4):106883, 2022. arXiv:2101.10797 [math.CT]), we define the contraderived category of a locally presentable abelian DG-category (textbf{B}) with enough projective objects and the coderived category of a Grothendieck abelian DG-category (textbf{A}). We construct the related abelian model category structures and show that the resulting exotic derived categories are well-generated. Then we specialize to the case of a locally coherent Grothendieck abelian DG-category (textbf{A}), and prove that its coderived category is compactly generated by the absolute derived category of finitely presentable objects of (textbf{A}), thus generalizing a result from the second-named author’s preprint (Št’ovíček in On purity and applications to coderived and singularity categories. arXiv:1412.1615 [math.CT]). In particular, the homotopy category of graded-injective left DG-modules over a DG-ring with a left coherent underlying graded ring is compactly generated by the absolute derived category of DG-modules with finitely presentable underlying graded modules. We also describe compact generators of the coderived categories of quasi-coherent matrix factorizations over coherent schemes.","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"34 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Tautological rings of Hilbert modular varieties 希尔伯特模态变的同调环

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-08-02 DOI: 10.1007/s00209-024-03560-2

Simon Cooper

引用次数: 0