Journal de Mathematiques Pures et Appliquees最新文献

英文中文

Waiting time solutions in gas dynamics 气体动力学中的等待时间解

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-09-30 DOI: 10.1016/j.matpur.2025.103806

Juhi Jang , Jiaqi Liu , Nader Masmoudi

In this article, we construct a continuum family of self-similar waiting time solutions for the one-dimensional compressible Euler equations for the adiabatic exponent

γ \in (1, 3)

in the half-line with the vacuum boundary. The solutions are confined by a stationary vacuum interface for a finite time with at least

C^{1}

regularity of the velocity and the sound speed up to the boundary. Subsequently, the solutions undergo the change of the behavior, becoming only Hölder continuous near the singular point, and simultaneously transition to the solutions to the vacuum moving boundary Euler equations satisfying the physical vacuum condition. When the boundary starts moving, a weak discontinuity emanating from the singular point along the sonic curve emerges. The solutions are locally smooth in the interior region away from the vacuum boundary and the sonic curve.

本文构造了具有绝热指数γ∈(1,3)的一维可压缩欧拉方程在真空边界半直线上的自相似等待时间解的连续统族。解被一个固定的真空界面限制在有限时间内，速度和声速在边界处至少呈C1规律。随后，解发生行为变化，仅在奇点附近Hölder连续，同时过渡到满足物理真空条件的真空移动边界欧拉方程的解。当边界开始移动时，从奇异点沿声波曲线发出的弱不连续出现。解在远离真空边界和声波曲线的内部区域是局部光滑的。

引用次数: 0

Monotonicity formulas for capillary surfaces 毛细管表面的单调性公式

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-09-30 DOI: 10.1016/j.matpur.2025.103802

Guofang Wang , Chao Xia , Xuwen Zhang

In this paper, we establish monotonicity formulas for capillary surfaces in the half-space

R_{+}^{3}

and in the unit ball

B^{3}

and extend the result of Volkmann (2016) [27] for surfaces with free boundary. As applications, we obtain Li-Yau-type inequalities for the Willmore energy of capillary surfaces, and extend Fraser-Schoen's optimal area estimate for minimal free boundary surfaces in

B^{3}

(2011) [10] to the capillary setting, which is different to another optimal area estimate proved by Brendle (2023) [5].

本文建立了半空间R+3和单位球B3中毛细曲面的单调性公式，推广了Volkmann(2016)[27]关于自由边界曲面的结果。作为应用，我们得到了毛细表面Willmore能量的li - yau型不等式，并将B3(2011)[10]中最小自由边界表面的Fraser-Schoen最优面积估计推广到毛细环境，这与Brendle(2023)[5]证明的另一种最优面积估计不同。

引用次数: 0

On the magnetic Dirichlet to Neumann operator on the exterior of the disk – Diamagnetism, weak-magnetic field limit and flux effects 圆盘表面的狄利克雷-诺伊曼算子——抗磁性、弱磁场极限和磁通效应

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-09-30 DOI: 10.1016/j.matpur.2025.103799

Bernard Helffer, François Nicoleau

In this paper, we analyze the magnetic Dirichlet-to-Neumann operator (D-to-N map)

\overset{ˇ}{Λ} (b, ν)

on the exterior of the disk with respect to a magnetic potential

A_{b, ν} = A^{b} + A_{ν}

where, for

b \in R

and

ν \in R

A^{b} (x, y) = b (- y, x)

and

A_{ν} (x, y)

is the Aharonov-Bohm potential centered at the origin of flux

2 π ν

. First, we show that the limit of

\overset{ˇ}{Λ} (b, ν)

b \to 0

is equal to the D-to-N map

\hat{Λ} (ν)

on the interior of the disk associated with the potential

A_{ν} (x, y)

. Secondly, we study the ground state energy of the D-to-N map

\overset{ˇ}{Λ} (b, ν)

and show that the strong diamagnetism property holds. Finally we slightly extend to the exterior case the asymptotic results as

b \to \infty

obtained in the interior case for general domains.

本文分析了圆盘外部磁势Ab，ν=Ab+ ν的磁Dirichlet-to-Neumann算子（D-to-N映射）Λ + (b,ν)，其中，对于b∈R和ν∈R， Ab(x,y)=b（- y,x）和ν(x,y)是以通量2πν为中心的Aharonov-Bohm势。首先，我们证明了Λ （b,ν）在b→0时的极限等于与势ν(x,y)相关联的磁盘内部的D-to-N映射Λ （ν）。其次，我们研究了D-to-N映射Λ （b,ν）的基态能量，证明了其强抗磁性。最后，我们将在一般区域的内情形下得到的b→∞渐近结果稍微推广到外情形。

引用次数: 0

On long time behavior of solutions of the Schrödinger-KdV system with and without resonant interactions 有和无共振相互作用时Schrödinger-KdV系统解的长时间行为

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-09-12 DOI: 10.1016/j.matpur.2025.103792

Deqin Zhou , Felipe Linares

<div><div>We consider the long time behavior of the solutions of the coupled Schrödinger-KdV system<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mi>i</mi><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>+</mo><msubsup><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mi>u</mi><mo>=</mo><mi>α</mi><mi>u</mi><mi>v</mi><mo>+</mo><mi>β</mi><mi>u</mi><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mspace></mspace><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mi>R</mi><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>v</mi><mo>+</mo><msubsup><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msubsup><mi>v</mi><mo>+</mo><mi>v</mi><msub><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow></msub><mi>v</mi><mo>=</mo><mi>γ</mi><msub><mrow><mo>∂</mo></mrow><mrow><mi>x</mi></mrow></msub><mo>(</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>,</mo><mspace></mspace><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mi>R</mi><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><msub><mrow><mo>|</mo></mrow><mrow><mi>t</mi><mo>=</mo><mn>0</mn></mrow></msub><mo>=</mo><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo><mo>.</mo></mtd></mtr></mtable></mrow></math></span></span></span> We show that global solutions to this system satisfy locally energy decay in a suitable interval, growing unbounded in time, in two situations. In the first case, we regard the parameter vector <span><math><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>γ</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>×</mo><mover><mrow><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow><mo>‾</mo></mover><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> without any size assumption on the initial data in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo><mo>×</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span>. In the second one, we consider the parameter vector <span><math><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>γ</mi><mo>)</mo><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>. In this case, we give a ‘‘smallness” criterion involving the product of the parameter −<em>β</em> and a constant depending on the initial data in <span><

我们考虑耦合Schrödinger-KdV系统{i∂tu+∂x2u=αuv+βu|u|2,(x,t)∈R×R+,∂tv+∂x3v+v∂xv=γ∂x(|u|2),(x,t)∈R×R+,(u,v)|t=0=(u0,v0)的长时间行为。在两种情况下，我们证明了该系统的全局解在一个适当的区间内满足局部能量衰减，并随时间无界增长。在第一种情况下，我们考虑参数向量(α,β,γ)∈R+×R+，对H1(R)×H1(R)中的初始数据没有任何大小假设。在第二个例子中，我们考虑参数向量(α,β,γ)∈R+×R−×R+。在这种情况下，我们给出了一个“小”准则，涉及参数- β和一个常数的乘积，这取决于H1(R)×H1(R)中的初始数据。我们的研究结果积极地回答了F. Linares， A. J. Mendez (2021) b[18]中提出的开放性问题。我们使用了与前一篇文章不同的新思路和技术。

引用次数: 0

Symplectic singularities arising from algebras of symmetric tensors 对称张量代数产生的辛奇异性

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-09-12 DOI: 10.1016/j.matpur.2025.103794

Baohua Fu , Jie Liu

The algebra of symmetric tensors

S (X) ≔ H^{0} (X, S^{•} T_{X})

of a projective manifold X leads to a natural dominant affinization morphism

φ_{X} : T^{⁎} X ⟶ Z_{X} ≔ Spec S (X) .

It is shown that

φ_{X}

is birational if and only if

T_{X}

is big. We prove that if

φ_{X}

is birational, then

Z_{X}

is a symplectic variety endowed with the Schouten–Nijenhuis bracket if and only if

P T_{X}

is of Fano type, which is the case for smooth projective toric varieties, smooth horospherical varieties with small boundary, and the quintic del Pezzo threefold. These give examples of a distinguished class of conical symplectic varieties, which we call symplectic orbifold cones.

对对称张量S(X)的代数，其中对投影流形X的H0（X,S•TX）是一个自然优势仿射态φX:T X ZX是一个自然优势仿射态。证明了φX当且仅当TX较大时是两位数的。证明了φX是双分型的，则当且仅当PTX为Fano型时，ZX是赋有Schouten-Nijenhuis括弧的简型变种，对于光滑投影环型变种、小边界光滑全球型变种和五次del Pezzo三重型都是如此。这些给出了一类特殊的圆锥辛变异体的例子，我们称之为辛轨道锥。

引用次数: 0

Cremona equivalence and log Kodaira dimension 克雷莫纳等价和对数柯达拉维数

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-09-12 DOI: 10.1016/j.matpur.2025.103793

Massimiliano Mella

Two projective varieties are said to be Cremona equivalent if there is a Cremona modification sending one onto the other. In the last decade, Cremona equivalence has been investigated widely, and we now have a complete theory for non-divisorial reduced schemes. The case of irreducible divisors is completely different, and not much is known besides the case of plane curves and a few classes of surfaces. In particular, for plane curves it is a classical result that an irreducible plane curve is Cremona equivalent to a line if and only if its log-Kodaira dimension is negative. This can be interpreted as the log version of Castelnuovo's rationality criterion for surfaces. One expects that a similar result for surfaces in projective space should not be true, as it is false, the generalization in higher dimensions of Castelnuovo's Rationality Theorem. In this paper, the first example of such behavior is provided, exhibiting a rational surface in the projective space with negative log-Kodaira dimension, which is not Cremona equivalent to a plane. This can be thought of as a sort of log Iskovkikh-Manin, Clemens-Griffith, Artin-Mumford example. Using this example, it is then possible to show that Cremona equivalence to a plane is neither open nor closed among log pairs with negative Kodaira dimension.

如果有一个克雷莫纳修改发送到另一个克雷莫纳，两个投影变种被称为克雷莫纳等效。在过去的十年里，克雷莫纳等价得到了广泛的研究，我们现在有了一个完整的非分约简格式理论。不可约因子的情况则完全不同，除了平面曲线和几类曲面的情况外，我们所知道的不多。特别地，对于平面曲线来说，当且仅当其log-Kodaira维为负时，一条不可约平面曲线与直线的克雷莫纳等价是一个经典的结果。这可以解释为Castelnuovo的表面合理性标准的对数版本。人们期望，对于投影空间中的曲面，类似的结果不应该是正确的，因为它是错误的，在更高的维度上推广Castelnuovo的合理性定理。本文给出了这种行为的第一个例子，给出了一个具有负log-Kodaira维数的投影空间中的有理曲面，该曲面不等价于平面。这可以看作是一种log Iskovkikh-Manin， Clemens-Griffith， Artin-Mumford的例子。利用这个例子，就有可能证明在具有负Kodaira维数的对数对中，平面的Cremona等价既不开也不闭。

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引用次数: 0

A Hamilton-Jacobi approach to road-field reaction-diffusion models 道路-场地反应-扩散模型的Hamilton-Jacobi方法

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-09-12 DOI: 10.1016/j.matpur.2025.103798

Christopher Henderson , King-Yeung Lam

We consider the road-field reaction-diffusion model introduced by Berestycki, Roquejoffre, and Rossi. By performing a “thin-front” limit, we are able to deduce a Hamilton-Jacobi equation with a suitable effective Hamiltonian on the road that governs the front location of the road-field model. Our main motivation is to apply the theory of strong (flux-limited) viscosity solutions in order to determine a control formulation interpretation of the front location. In view of the ecological meaning of the road-field model, this is natural as it casts the invasion problem as one of finding optimal paths that balance the positive growth rate in the field with the fast diffusion on the road.

Our main contribution is a nearly complete picture of the behavior on two-road conical domains. When the diffusivities on each road are the same, we show that the propagation speed in each direction in the cone can be computed via those associated with one-road half-space problem. When the diffusivities differ, we show that the speed along the faster road is unchanged, while the speed along the slower road can be enhanced. Along the way we provide a new proof of known results on the one-road half-space problem via our approach.

我们考虑由Berestycki、Roquejoffre和Rossi引入的道路-场地反应-扩散模型。通过执行“薄前”限制，我们能够在道路上推导出具有适当有效哈密顿量的汉密尔顿-雅可比方程，该哈密顿量控制着路场模型的前方位置。我们的主要动机是应用强（通量限制）粘度解的理论，以确定对锋面位置的控制公式解释。考虑到路场模型的生态学意义，这是很自然的，因为它将入侵问题视为寻找最优路径的问题之一，以平衡领域中的正增长率和道路上的快速扩散。我们的主要贡献是几乎完整地描绘了双路圆锥域的行为。当每条道路上的扩散系数相同时，我们证明了锥内每个方向的传播速度可以通过与一条道路半空间问题相关的传播速度来计算。当扩散系数不同时，我们发现沿较快道路的速度不变，而沿较慢道路的速度可以提高。在此过程中，我们通过我们的方法为单向半空间问题的已知结果提供了新的证明。

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引用次数: 0

Suppression of blow-up by local anisotropy of signal production in the Keller-Segel system Keller-Segel系统中信号产生的局部各向异性抑制爆破

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-09-12 DOI: 10.1016/j.matpur.2025.103795

Youshan Tao , Michael Winkler

In a smoothly bounded domain

Ω \subset R^{n}

n \leq 5

, and with

D > 0

and

d > 0

, this manuscript considers the Neumann initial-boundary problem for the Keller-Segel type system

{\begin{matrix} u_{t} = D Δ u - \nabla \cdot (u \nabla v), \\ v_{t} = d Δ v + \nabla \cdot (u \nabla v) - v + u, \end{matrix} (⋆)

which arises in the modeling for chemotactic movement in the presence of certain anisotropic signal production mechanisms.

Unlike the classical Keller-Segel model whose solutions may blow up in finite time in high-dimensional domains, this problem is shown to admit a unique global bounded classical solution whenever the difference

| D - d |

is appropriately small. This markedly distinguishes (⋆) from classical Keller-Segel systems for which some solutions are known to blow up in finite time when

n \geq 2

在光滑有界域Ω∧Rn， n≤5，并且D>；0和D>；0中，本文考虑了Keller-Segel型系统{ut=DΔu−∇⋅(u∇v),vt=dΔv+∇⋅(u∇v)−v+u,（-）的Neumann初始边界问题，该问题出现在存在某些各向异性信号产生机制的趋化运动建模中。与经典Keller-Segel模型的解在高维域中可能在有限时间内爆炸不同，当差分|D - D |适当小时，该问题承认一个唯一的全局有界经典解。这明显区别于经典的Keller-Segel系统，对于经典的Keller-Segel系统，已知当n≥2时，某些解会在有限时间内爆炸。

引用次数: 0

Spectral analysis and phase transitions for long-range interactions in harmonic chains of oscillators 谐振子谐波链中远距离相互作用的频谱分析和相变

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-09-12 DOI: 10.1016/j.matpur.2025.103796

Simon Becker , Angeliki Menegaki , Jiming Yu

We consider chains of N harmonic oscillators in two dimensions coupled to a Langevin heat reservoir at fixed temperature, a classical model for heat conduction introduced by Lebowitz, Lieb, and Rieder (1967). We extend our previous results (Becker and Menegaki, 2021) significantly by providing a full spectral description of the full Fokker-Planck operator, also allowing for the presence of a constant external magnetic field for charged oscillators. We then study oscillator chains with additional next-to-nearest-neighbor interactions and find that the spectral gap undergoes a phase transition if the next-to-nearest-neighbor interactions are sufficiently strong and may even cease to exist for oscillator chains of finite length.

我们考虑二维N个谐振子链与固定温度下的朗之万热源耦合，朗之万热源是Lebowitz， Lieb和Rieder（1967）引入的热传导经典模型。我们扩展了之前的结果（Becker和Menegaki， 2021），提供了完整的福克-普朗克算子的全光谱描述，也允许带电振荡器存在恒定的外部磁场。然后，我们研究了具有额外的次近邻相互作用的振子链，发现如果次近邻相互作用足够强，谱隙会经历相变，对于有限长度的振子链甚至可能不存在谱隙。

引用次数: 0

Global regularity of integral 2-varifolds with square integrable mean curvature 平均曲率平方可积的积分2-变量的全局正则性

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-09-12 DOI: 10.1016/j.matpur.2025.103797

Fabian Rupp , Christian Scharrer

We provide sharp sufficient criteria for an integral 2-varifold to be induced by a

W^{2, 2}

-conformal immersion of a smooth surface. Our approach is based on a fine analysis of the Hausdorff density for 2-varifolds with critical integrability of the mean curvature and a recent local regularity result by Bi–Zhou. In codimension one, there are only three possible density values below 2, each of which can be attained with equality in the Li–Yau inequality for the Willmore functional by the unit sphere, the double bubble, and the triple bubble. We show that below an optimal threshold for the Willmore energy, a varifold induced by a current without boundary is in fact a curvature varifold with a uniform bound on its second fundamental form. Consequently, the minimization of the Willmore functional in the class of curvature varifolds with prescribed even Euler characteristic provides smooth solutions for the Willmore problem. In particular, the “ambient” varifold approach and the “parametric” approach are equivalent for minimizing the Willmore energy.

我们提供了由光滑表面的w2,2 -保形浸没诱导出的积分2-变形的充分准则。我们的方法是基于对具有平均曲率临界可积性的2-变量的Hausdorff密度的精细分析和Bi-Zhou最近的局部正则性结果。在余维1中，小于2的密度值只有三种可能，每一种密度值都可以通过单位球、双泡和三重泡在Willmore泛函的Li-Yau不等式中得到。我们证明了在Willmore能量的最佳阈值以下，由无边界电流诱导的变量实际上是在其第二基本形式上具有均匀边界的曲率变量。因此，在具有规定的偶欧拉特征的曲率变分类中，Willmore泛函的最小化为Willmore问题提供了光滑解。特别是，“环境”变形方法和“参数”方法对于最小化Willmore能量是等效的。

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