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Asymptotics for the rotating fluids and primitive systems with large ill-prepared initial data in critical spaces 临界空间中初始数据不充分的旋转流体和原始系统的渐近性
IF 0.9 Q2 MATHEMATICS Pub Date : 2022-04-12 DOI: 10.2140/tunis.2023.5.171
Frédéric Charve
In this article we study the lifespan and asymptotics (in the large rotation and stratification regime) for the Primitive system for highly ill-prepared initial data in critical spaces. Compared to our previous works, we simplified the proof and made it adaptable to the Rotating fluids system with highly ill-prepared initial data decomposed as a sum of 2D horizontal part and a very large 3D part. We also provide explicit convergence rates.
在本文中,我们研究了原始系统的寿命和渐近性(在大旋转和分层状态下)对于临界空间中高度准备不足的初始数据。与我们以前的工作相比,我们简化了证明,使其适用于旋转流体系统,初始数据分解为二维水平部分和非常大的三维部分的总和。我们还提供了明确的收敛率。
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引用次数: 1
Quasi-2-Segal sets Quasi-2-Segal集
IF 0.9 Q2 MATHEMATICS Pub Date : 2022-04-05 DOI: 10.2140/tunis.2023.5.327
M. Feller
We show that the 2-Segal spaces (also called decomposition spaces) of Dyckerhoff-Kapranov and G'alvez-Kock-Tonks have a natural analogue within simplicial sets, which we call quasi-2-Segal sets, and that the two ideas enjoy a similar relationship as the one Segal spaces have with quasi-categories. In particular, we construct a model structure on the category of simplicial sets whose fibrant objects are the quasi-2-Segal sets which is Quillen equivalent to a model structure for complete 2-Segal spaces (where our notion of completeness comes from one of the equivalent characterizations of completeness for Segal spaces). We also prove a path space criterion, which says that a simplicial set is a quasi-2-Segal set if and only if its path spaces (also called d'ecalage) are quasi-categories, as well as an edgewise subdivision criterion.
我们证明了Dyckerhoff-Kapranov和G'alvez-Kock-Tonks的2-Segal空间(也称为分解空间)在简单集(我们称之为拟2-Segal集)内具有自然的类似,并且这两个思想与Segal空间与拟范畴的关系相似。特别地,我们在以拟2-Segal集为对象的简单集的范畴上构造了一个模型结构,它与完全2-Segal空间的模型结构是Quillen等价的(其中我们的完备性概念来自于Segal空间完备性的等价表征之一)。我们还证明了一个路径空间准则,即当且仅当一个简单集的路径空间(也称为d'ecalage)是拟范畴时,它是一个拟2- segal集,以及一个边缘细分准则。
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引用次数: 3
Partially algebraic maps and operator algebras 部分代数映射与算子代数
IF 0.9 Q2 MATHEMATICS Pub Date : 2022-03-30 DOI: 10.2140/tunis.2022.4.1
M. Karoubi
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引用次数: 0
Uniformity of rational points: an up-date and corrections 有理点的一致性:更新和修正
IF 0.9 Q2 MATHEMATICS Pub Date : 2022-03-30 DOI: 10.2140/tunis.2022.4.183
L. Caporaso, J. Harris, B. Mazur
In [2] it is asserted that, assuming the truth of the Strong Lang Conjecture (Conjecture 1 below), a very strong form of boundedness holds: for every g ≥ 2 there is a finite bound N(g)—not depending on K!—such that for any number field K there are only finitely many isomorphism classes of curves of genus g defined over K with more than N(g) K-rational points. The issue is, in that statement do we mean finitely many isomorphism classes over K, or over the algebraic closure K? The paper asserts the statement in the stronger form—up to isomorphism over K—but the proof establishes only the weaker statement that there are finitely many curves with more than N(g) points up to isomorphism over K.
在[2]中,我们断言,假设强朗猜想(下面的猜想1)成立,一个非常强的有界性形式成立:对于每一个g≥2,存在一个有限界N(g) -不依赖于K!-使得对于任意数域K,只有有限多个在K上定义的g属曲线的同构类具有大于N(g)个K-有理点。问题是,在这个表述中我们是指K上,还是代数闭包K上,有有限多个同构类吗?本文以较强的形式证明了K上同构的命题,但证明只建立了较弱的命题,即有有限多条大于N(g)的曲线指向K上同构。
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引用次数: 2
Constructibilité générique et uniformité enℓ 通用可建性和统一性,ℓ
IF 0.9 Q2 MATHEMATICS Pub Date : 2022-03-30 DOI: 10.2140/tunis.2022.4.159
L. Illusie
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引用次数: 1
Uniform observation of semiclassicalSchrödinger eigenfunctions on an interval 区间上半经典薛定谔本征函数的一致观测
IF 0.9 Q2 MATHEMATICS Pub Date : 2022-03-07 DOI: 10.2140/tunis.2023.5.125
Camille Laurent, Matthieu Léautaud
We consider eigenfunctions of a semiclassical Schr{"o}dinger operator on an interval, with a single-well type potential and Dirichlet boundary conditions. We give upper/lower bounds on the L^2 density of the eigenfunctions that are uniform in both semiclassical and high energy limits. These bounds are optimal and are used in an essential way in a companion paper in application to a controllability problem. The proofs rely on Agmon estimates and a Gronwall type argument in the classically forbidden region, and on the description of semiclassical measures for boundary value problems in the classically allowed region. Limited regularity for the potential is assumed.
我们考虑半经典Schr的本征函数区间上的dinger算子,具有单阱型势和Dirichlet边界条件。我们给出了本征函数的L^2密度的上/下界,这些本征函数在半经典和高能极限下都是一致的。这些边界是最优的,并且在应用于可控性问题的配套论文中以重要的方式使用。证明依赖于经典禁域中的Agmon估计和Gronwall型论证,以及经典允许域中边值问题的半经典测度的描述。假设电势具有有限的规律性。
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引用次数: 6
Hodge properties of Airy moments Airy矩的Hodge性质
IF 0.9 Q2 MATHEMATICS Pub Date : 2021-12-26 DOI: 10.2140/tunis.2023.5.215
C. Sabbah, Jeng-Daw Yu
We consider the complex analogues of symmetric power moments of cubic exponential sums. These are symmetric powers of the classical Airy differential equation. We show that their de Rham cohomologies underlie an arithmetic Hodge structure in the sense of Anderson and we compute their Hodge numbers by means of the irregular Hodge filtration, which is indexed by rational numbers, on their realizations as exponential mixed Hodge structures. The main result is that all Hodge numbers are either zero or one.
我们考虑三次指数和的对称幂矩的复类似物。这些是经典艾里微分方程的对称幂。我们证明了他们的de Rham上同调是Anderson意义上的算术Hodge结构的基础,并且我们通过由有理数索引的不规则Hodge滤波来计算他们的Hodge数,在他们实现为指数混合Hodge结构时。主要结果是所有的霍奇数要么是零要么是一。
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引用次数: 2
Singular limit of an Allen–Cahn equation withnonlinear diffusion 具有非线性扩散的Allen–Cahn方程的奇异极限
IF 0.9 Q2 MATHEMATICS Pub Date : 2021-12-24 DOI: 10.2140/tunis.2022.4.719
Perla El Kettani, T. Funaki, D. Hilhorst, Hyunjoo Park, S. Sethuraman
We consider an Allen-Cahn equation with nonlinear diffusion, motivated by the study of the scaling limit of certain interacting particle systems. We investigate its singular limit and show the generation and propagation of an interface in the limit. The evolution of this limit interface is governed by mean curvature flow with a novel, homogenized speed in terms of a surface tension-mobility parameter emerging from the nonlinearity in our equation.
我们考虑了一个具有非线性扩散的Allen-Cahn方程,其动机是研究某些相互作用粒子系统的标度极限。我们研究了它的奇异极限,并给出了极限中界面的产生和传播。根据我们方程中的非线性产生的表面张力迁移率参数,该极限界面的演变由平均曲率流控制,该平均曲率流具有新颖的均匀速度。
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引用次数: 3
Rigidity aspects of singular patches in stratified flows 分层流动中奇异斑块的刚性方面
IF 0.9 Q2 MATHEMATICS Pub Date : 2021-11-14 DOI: 10.2140/tunis.2022.4.465
T. Hmidi, Haroune Houamed, M. Zerguine
We explore the local well-posedness theory for the 2d inviscid Boussinesq system when the vorticity is given by a singular patch. We give a significant improvement of cite{Hassainia-Hmidi} by replacing their compatibility assumption on the density with a constraint on its platitude degree on the singular set. The second main contribution focuses on the same issue for the partial viscous Boussinesq system. We establish a uniform LWP theory with respect to the vanishing conductivity. This issue is much more delicate than the inviscid case and one should carefully deal with various difficulties related to the diffusion effects which tend to alter some local structures. The weak a priori estimates are not trivial and refined analysis on transport-diffusion equation subject to a logarithmic singular potential is required. Another difficulty stems from some commutators arising in the control of the co-normal regularity that we counterbalance in part by the maximal smoothing effects of transport-diffusion equation advected by a velocity field which scales slightly below the Lipschitz class.
研究了二维无粘Boussinesq系统在涡度由奇异块给出时的局部适定性理论。我们将cite{Hassainia-Hmidi}在密度上的相容性假设替换为其在奇异集上的重复度约束,从而对其进行了显著改进。第二个主要贡献集中在部分粘性Boussinesq系统的相同问题上。我们建立了关于电导率消失的统一LWP理论。这个问题比不粘的情况要微妙得多,人们应该仔细处理与扩散效应有关的各种困难,扩散效应往往会改变一些局部结构。弱先验估计不是微不足道的,需要对对数奇异势作用下的输运-扩散方程进行精细化分析。另一个困难来自于在控制共正态规则时产生的一些换向子,我们通过一个尺度略低于Lipschitz类的速度场平流的输运-扩散方程的最大平滑效应来部分地抵消这些换向子。
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引用次数: 3
Moduli of local shtukas and Harris’sconjecture 局部shtukas模与Harri猜想
IF 0.9 Q2 MATHEMATICS Pub Date : 2021-10-20 DOI: 10.2140/tunis.2021.3.749
D. Hansen
We prove, under a certain assumption of “Hodge-Newton reducibility”, a strong form of a conjecture of Harris on the cohomology of moduli spaces of mixed-characteristic local shtukas for GLn. Our strategy is roughly based on a previous strategy developed by Mantovan in the setting of p-divisible groups, but the arguments are completely different. In particular, we reinterpret and generalize the Hodge-Newton filtration of a p-divisible group in terms of modified vector bundles on the Fargues-Fontaine curve. We also compute the dualizing complex and compactly supported étale cohomology of any positive Banach-Colmez space over any base; this should be of independent interest.
在“Hodge-Newton可约性”的一定假设下,我们证明了Harris关于GLn的混合特征局部shtukas模空间的上同调猜想的一个强形式。我们的策略大致基于Mantovan之前在p-可分群的设置中开发的策略,但论点完全不同。特别地,我们用Fargues-Fontaine曲线上的修正向量丛重新解释和推广了p-可分群的Hodge-Newton滤。我们还计算了任意基上任意正Banach Colmez空间的对偶复紧支撑étale上同调;这应该是独立的利益。
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引用次数: 7
期刊
Tunisian Journal of Mathematics
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