Forum of Mathematics Sigma最新文献

Axisymmetric Incompressible Viscous Plasmas: Global Well-Posedness and Asymptotics 轴对称不可压缩粘性等离子体：全局拟然性和渐近性

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-09-10 DOI: 10.1017/fms.2024.60

Diogo Arsénio, Zineb Hassainia, Haroune Houamed

{"title":"Axisymmetric Incompressible Viscous Plasmas: Global Well-Posedness and Asymptotics","authors":"Diogo Arsénio, Zineb Hassainia, Haroune Houamed","doi":"10.1017/fms.2024.60","DOIUrl":"https://doi.org/10.1017/fms.2024.60","url":null,"abstract":"This paper is devoted to the global analysis of the three-dimensional axisymmetric Navier–Stokes–Maxwell equations. More precisely, we are able to prove that, for large values of the speed of light $cin (c_0, infty )$ , for some threshold $c_0>0$ depending only on the initial data, the system in question admits a unique global solution. The ensuing bounds on the solutions are uniform with respect to the speed of light, which allows us to study the singular regime $crightarrow infty $ and rigorously derive the limiting viscous magnetohydrodynamic (MHD) system in the axisymmetric setting. The strategy of our proofs draws insight from recent results on the two-dimensional incompressible Euler–Maxwell system to exploit the dissipative–dispersive structure of Maxwell’s system in the axisymmetric setting. Furthermore, a detailed analysis of the asymptotic regime $cto infty $ allows us to derive a robust nonlinear energy estimate which holds uniformly in c. As a byproduct of such refined uniform estimates, we are able to describe the global strong convergence of solutions toward the MHD system. This collection of results seemingly establishes the first available global well-posedness of three-dimensional viscous plasmas, where the electric and magnetic fields are governed by the complete Maxwell equations, for large initial data as $cto infty $ .","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196935","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}

引用次数: 0

Stability in the category of smooth mod-p representations of 光滑模-p 表示类别中的稳定性

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-09-09 DOI: 10.1017/fms.2024.37

Konstantin Ardakov, Peter Schneider

引用次数: 0

Bounds on multiplicities of symmetric pairs of finite groups 有限群对称对的乘数界值

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-09-09 DOI: 10.1017/fms.2024.58

Avraham Aizenbud, Nir Avni

引用次数: 0

Pressure of a dilute spin-polarized Fermi gas: Lower bound 稀释自旋极化费米气体的压力：下限

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-09-09 DOI: 10.1017/fms.2024.56

Asbjørn Bækgaard Lauritsen, Robert Seiringer

{"title":"Pressure of a dilute spin-polarized Fermi gas: Lower bound","authors":"Asbjørn Bækgaard Lauritsen, Robert Seiringer","doi":"10.1017/fms.2024.56","DOIUrl":"https://doi.org/10.1017/fms.2024.56","url":null,"abstract":"We consider a dilute fully spin-polarized Fermi gas at positive temperature in dimensions $din {1,2,3}$ . We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order $a^drho ^{2+2/d}$ , where a is the p-wave scattering length of the repulsive interaction and $rho $ is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237–260).","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196936","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}

引用次数: 0

On the local -Bound of the Eisenstein series 关于爱森斯坦数列的局部束缚

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-09-06 DOI: 10.1017/fms.2024.59

Subhajit Jana, Amitay Kamber

{"title":"On the local -Bound of the Eisenstein series","authors":"Subhajit Jana, Amitay Kamber","doi":"10.1017/fms.2024.59","DOIUrl":"https://doi.org/10.1017/fms.2024.59","url":null,"abstract":"We study the growth of the local $L^2$ -norms of the unitary Eisenstein series for reductive groups over number fields, in terms of their parameters. We derive a poly-logarithmic bound on an average, for a large class of reductive groups. The method is based on Arthur’s development of the spectral side of the trace formula, and ideas of Finis, Lapid and Müller. As applications of our method, we prove the optimal lifting property for $mathrm {SL}_n(mathbb {Z}/qmathbb {Z})$ for square-free q, as well as the Sarnak–Xue [52] counting property for the principal congruence subgroup of $mathrm {SL}_n(mathbb {Z})$ of square-free level. This makes the recent results of Assing–Blomer [8] unconditional.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196940","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}

引用次数: 0

Flags of sheaves, quivers and symmetric polynomials 剪切、四元组和对称多项式的标志

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-09-06 DOI: 10.1017/fms.2024.43

Giulio Bonelli, Nadir Fasola, Alessandro Tanzini

引用次数: 0

A proof of the Elliott–Rödl conjecture on hypertrees in Steiner triple systems 关于斯坦纳三重系统中肥大树的埃利奥特-罗德尔猜想的证明

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-09-06 DOI: 10.1017/fms.2024.34

Seonghyuk Im, Jaehoon Kim, Joonkyung Lee, Abhishek Methuku

{"title":"A proof of the Elliott–Rödl conjecture on hypertrees in Steiner triple systems","authors":"Seonghyuk Im, Jaehoon Kim, Joonkyung Lee, Abhishek Methuku","doi":"10.1017/fms.2024.34","DOIUrl":"https://doi.org/10.1017/fms.2024.34","url":null,"abstract":"Hypertrees are linear hypergraphs where every two vertices are connected by a unique path. Elliott and Rödl conjectured that for any given $mu>0$ , there exists $n_0$ such that the following holds. Every n-vertex Steiner triple system contains all hypertrees with at most $(1-mu )n$ vertices whenever $ngeq n_0$ . We prove this conjecture.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196939","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}

引用次数: 0

Persistent transcendental Bézout theorems 持久超越贝祖特定理

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-08-27 DOI: 10.1017/fms.2024.49

Lev Buhovsky, Iosif Polterovich, Leonid Polterovich, Egor Shelukhin, Vukašin Stojisavljević

引用次数: 0

Sums of squares, Hankel index and almost real rank 平方和、汉克尔指数和几乎实等级

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-05-30 DOI: 10.1017/fms.2024.45

Grigoriy Blekherman, Justin Chen, Jaewoo Jung

{"title":"Sums of squares, Hankel index and almost real rank","authors":"Grigoriy Blekherman, Justin Chen, Jaewoo Jung","doi":"10.1017/fms.2024.45","DOIUrl":"https://doi.org/10.1017/fms.2024.45","url":null,"abstract":"The Hankel index of a real variety X is an invariant that quantifies the difference between nonnegative quadrics and sums of squares on X. In [5], the authors proved an intriguing bound on the Hankel index in terms of the Green–Lazarsfeld index, which measures the ‘linearity’ of the minimal free resolution of the ideal of X. In all previously known cases, this bound was tight. We provide the first class of examples where the bound is not tight; in fact, the difference between Hankel index and Green–Lazarsfeld index can be arbitrarily large. Our examples are outer projections of rational normal curves, where we identify the center of projection with a binary form F. The Green–Lazarsfeld index of the projected curve is given by the complex Waring border rank of F [16]. We show that the Hankel index is given by the almost real rank of F, which is a new notion that comes from decomposing F as a sum of powers of almost real forms. Finally, we determine the range of possible and typical almost real ranks for binary forms.","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141193097","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}

引用次数: 0

L-invariants for cohomological representations of PGL(2) over arbitrary number fields 任意数域上 PGL(2) 同调表示的 L 不变式

IF 1.7 2区数学

Forum of Mathematics Sigma Pub Date : 2024-05-30 DOI: 10.1017/fms.2024.51

Lennart Gehrmann, Maria Rosaria Pati

引用次数: 0