Journal de Mathematiques Pures et Appliquees最新文献

英文中文

L2 estimates and existence theorems for the ∂‾ operators in infinite dimensions, II 无穷维∂∂算子的L2估计和存在性定理，II

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-10-16 DOI: 10.1016/j.matpur.2025.103811

Zhouzhe Wang , Jiayang Yu , Xu Zhang

This paper is the second part of our series of works to establish

L^{2}

estimates and existence theorems for the

\overline{\partial}

operators in infinite dimensions. In this part, we consider the most difficult case, i.e., the underlying space is a general pseudo-convex domain. In order to handle this longstanding unsolved problem, we introduce several new concepts and techniques, which have independent interest and may be applied in other places.

本文是我们建立无穷维∂∂算子的L2估计和存在性定理系列工作的第二部分。在这一部分中，我们考虑最困难的情况，即底层空间是一个一般的伪凸域。为了解决这个长期未解决的问题，我们引入了一些新的概念和技术，这些概念和技术具有独立的兴趣，可以在其他地方应用。

引用次数: 0

Controllability of a coupled wave system with a single control and different speeds 单控不同速度耦合波系统的可控性

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-10-16 DOI: 10.1016/j.matpur.2025.103808

Pierre Lissy , Jingrui Niu

We consider an exact controllability problem in a smooth bounded domain Ω of

R^{d}

d \in N^{⁎}

, for a coupled wave system, with two different speeds and a single control acting on an open subset ω satisfying the Geometric Control Condition and acting on one speed only. Actions for the wave equations with the second speed are obtained through a coupling term. Firstly, we construct appropriate state spaces with compatibility conditions associated with the coupling structure. Secondly, in these well-prepared spaces, we prove that the coupled wave system is exactly controllable if and only if the coupling structure satisfies an operator Kalman rank condition.

考虑一个耦合波系统在Rd， d∈N的光滑有界域Ω上的精确可控性问题，该系统具有两个不同的速度和一个控制作用于满足几何控制条件且仅作用于一个速度的开放子集Ω。二阶波方程的作用通过耦合项得到。首先，我们构造了适当的状态空间，并给出了与耦合结构相关联的相容条件。其次，在这些充分准备的空间中，我们证明了当且仅当耦合结构满足算子卡尔曼秩条件时，耦合波系统是精确可控的。

引用次数: 0

Isotrivial Lagrangian fibrations of compact hyper-Kähler manifolds 紧致hyper-Kähler流形的等平凡拉格朗日颤振

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-10-16 DOI: 10.1016/j.matpur.2025.103810

Yoon-Joo Kim , Radu Laza , Olivier Martin

This article initiates the study of isotrivial Lagrangian fibrations of compact hyper-Kähler manifolds. We present four foundational results that extend well-known facts about isotrivial elliptic fibrations of K3 surfaces. First, we prove that smooth fibers of an isotrivial Lagrangian fibration are isogenous to a power of an elliptic curve. Second, we exhibit a dichotomy between two types of isotrivial Lagrangian fibrations, which we call A and B. Third, we give a classification result for type A isotrivial Lagrangian fibrations. Namely, if a type A isotrivial Lagrangian fibration admits a rational section, then it is birational to one of two straightforward examples of isotrivial fibrations of hyper-Kähler manifolds of

{K3}^{[n]}

-type and

{Kum}_{n}

-type. Finally, we prove that a genericity assumption on the smooth fiber of an isotrivial Lagrangian fibration without multiple fibers ensures that the fibration is of type A.

本文开始研究紧致hyper-Kähler流形的等平凡拉格朗日振动。我们提出了四个基本结果，这些结果扩展了众所周知的关于K3表面的等平凡椭圆振动的事实。首先，我们证明了等平凡拉格朗日纤维的光滑纤维在椭圆曲线的幂次上是等均匀的。其次，我们展示了两种类型的等平凡拉格朗日纤维的二分类，我们称之为a和b。第三，我们给出了a型等平凡拉格朗日纤维的分类结果。也就是说，如果a型等平凡拉格朗日纤摇允许有一个理性截面，那么它与K3[n]型和kumn型hyper-Kähler流形等平凡纤摇的两个简单例子之一是同源的。最后，我们证明了无多根纤维的等平凡拉格朗日纤维的光滑纤维的一般性假设保证了该纤维为a型纤维。

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引用次数: 0

The spectral eigenvalue set and Beurling dimension on self-similar measures 自相似测度上的谱特征值集和伯林维数

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-10-15 DOI: 10.1016/j.matpur.2025.103809

Lu Zheng-Yi

In this work, we study harmonic analysis in self-similar measures. A set

A

is called a spectral eigenvalue set of μ if there exists

Λ \subset R

such that the family

{a Λ : a \in A}

are spectra for μ. Given a Hadamard triple

(q, D, L)

, Łaba and Wang [33] proved that the associated self-similar measure

μ_{q, D}

is spectral. We establish that the set

T = {t \in Z : (q, D, t L) forms a Hadamard triple} \supseteq {p \in Z : \gcd (p, q) = 1}

constitutes a spectral eigenvalue set for

μ_{q, D}

. Furthermore, we demonstrate that for any prescribed Beurling dimension

s \in [0, \frac{\log # D}{\log q}]

, the corresponding spectra have the cardinality of the continuum. This result provides a complete answer to the question posed by Kong, Li and Wang [30]. As an application, we characterize the eigenvalue sets for N-Bernoulli convolutions, proving that

A

is an eigenvalue set if and only if

A \subseteq \frac{1}{T} T

for some

T \in T

本文主要研究自相似测度中的谐波分析。如果存在Λ∧R使得族{aΛ： A∈A}是μ的谱，则集合A称为μ的谱特征值集。给出一个Hadamard三重体（q，D，L）， Łaba和Wang[33]证明了相关的自相似测度μq，D是谱的。我们建立了setT={t∈Z:（q，D,tL）构成一个Hadamard三重体}{p∈Z:gcd (p,q)=1}构成μq，D的谱特征值集。进一步证明了对于任意给定的Beurling维数s∈[0，log (#) log (q)]，对应的谱具有连续统的基数性。这一结果为Kong， Li和Wang b[30]提出的问题提供了完整的答案。作为应用，我们对N-Bernoulli卷积的特征值集进行了刻画，证明了对于某T∈T， A是一个当且仅当A≠1TT的特征值集。

引用次数: 0

From KP-I lump solution to travelling waves of Gross-Pitaevskii equation 从Gross-Pitaevskii方程的KP-I块解到行波

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-10-03 DOI: 10.1016/j.matpur.2025.103801

Yong Liu , Zhengping Wang , Juncheng Wei , Wen Yang

Let q be a nondegenerate lump type solution to the KP-I (Kadomtsev-Petviashvili-I) equation

\partial_{x}^{4} q - 2 \sqrt{2} \partial_{x}^{2} q - 3 \sqrt{2} \partial_{x} ({(\partial_{x} q)}^{2}) - 2 \partial_{y}^{2} q = 0 .

We show the existence of travelling wave solutions with the form

u_{ε} (x - c t, y)

, for the GP (Gross-Pitaevskii) equation

i \partial_{t} Ψ + Δ Ψ + (1 - | Ψ |^{2}) Ψ = 0 in R^{2},

with travelling speed

c = \sqrt{2} - ε^{2}

, and

u_{ε} = 1 + i ε q + O (ε^{2})

. This proves the existence of finite energy solutions in the so-called Jones-Roberts program within the transonic regime

c \in (\sqrt{2} - ε^{2}, \sqrt{2})

. The main ingredients in our proof are detailed point-wise estimates for the Green functions associated to a family of fourth order hypoelliptic operators. In view of the classification of lump type solutions of the KP-I equation, our proof also indicates that for fixed small ε, there should exist a sequence of travelling wave solutions to GP equation, with energy tends to infinity.

设q是KP-I （Kadomtsev-Petviashvili-I）方程∂x4q−22∂x2q−32∂x((∂xq)2)−2∂y2q=0的非简并块型解。我们证明了GP （Gross-Pitaevskii）方程∂tΨ+ΔΨ+（1−|Ψ|2）Ψ=0inR2的行波解的存在性，其行波解的形式为uε(x−ct,y)，行进速度c=2−ε2，且uε=1+iεq+O（ε2）。这证明了所谓的Jones-Roberts规划在跨声速区间c∈(2−ε2,2)内有限能量解的存在性。我们证明的主要成分是与一组四阶半椭圆算子相关的Green函数的详细点估计。鉴于KP-I方程块状解的分类，我们的证明还表明，对于固定的小ε， GP方程的行波解应该存在一个序列，且能量趋于无穷。

引用次数: 0

Global axisymmetric solution to the 3D incompressible anisotropic Navier–Stokes equations 三维不可压缩各向异性Navier-Stokes方程的全局轴对称解

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-10-01 DOI: 10.1016/j.matpur.2025.103807

Hui Chen , Zijin Li , Ping Zhang

In this paper, we prove the global existence and uniqueness of axisymmetric solution to the 3D incompressible anisotropic Navier–Stokes equations in a cylindrical domain with Navier boundary condition provided that the swirl component of the initial velocity is sufficiently small. The main idea of the proof is to perform energy estimates for the pair

(J, Ω^{c})

, where

and

is a corrector of

. In order to close the energy estimates, we introduced the derivative-reduction technique and new elliptic estimates of the pressure function, which are established to overcome difficulties arising from the lower-order terms in the Navier boundary condition. We also consider the global regularity of the axisymmetric solution to the Navier–Stokes equations with full viscosity subject to the total-slip Navier boundary condition. Several new inequalities are established to address the challenges posed by the weak horizontal diffusion of the swirl component.

本文在初始速度的旋流分量足够小的条件下，证明了三维不可压缩各向异性Navier - stokes方程在圆柱域上轴对称解的整体存在唯一性。证明的主要思想是对（J，Ωc）进行能量估计，其中和是的校正器。为了关闭能量估计，我们引入了导数约简技术和新的压力函数椭圆估计，这是为了克服Navier边界条件中低阶项所带来的困难而建立的。同时考虑了全滑移Navier边界条件下具有全黏度的Navier - stokes方程轴对称解的全局正则性。建立了几个新的不等式来解决涡流分量的弱水平扩散所带来的挑战。

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引用次数: 0

Fabes-Stroock approach to higher integrability of Green's functions and ABP estimates with Ld drift Green函数高可积性的Fabes-Stroock方法及Ld漂移下的ABP估计

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-10-01 DOI: 10.1016/j.matpur.2025.103805

Pilgyu Jung , Kwan Woo

We explore the higher integrability of Green's functions associated with the second-order elliptic equation

a^{i j} D_{i j} u + b^{i} D_{i} u = f

in a bounded domain

Ω \subset R^{d}

, and establish an enhanced version of Aleksandrov's maximum principle. In particular, we consider the drift term

b = (b^{1}, \dots, b^{d})

L_{d}

and the source term

f \in L_{p}

for some

p < d

. This provides an alternative and analytic proof of a result by N.V. Krylov (Ann. Probab., 2021) concerning

L_{d}

drifts. The key step involves deriving a Gehring-type inequality for Green's functions by using the Fabes-Stroock approach (Duke Math. J., 1984).

我们探索了二阶椭圆方程aijDiju+biDiu=f在有界域Ω∧Rd上的格林函数的高可积性，并建立了Aleksandrov极大原理的增强版本。特别地，我们考虑Ld中的漂移项b=（b1，…，bd）和某些p<；d的源项f∈Lp。这为N.V. Krylov (Ann。Probab。（2021）关于Ld漂移。关键的一步是通过使用Fabes-Stroock方法（杜克数学）推导格林函数的格林型不等式。J。,1984)。

引用次数: 0

Derivation of Hartree theory for two-dimensional attractive Bose gases in almost Gross–Pitaevskii regime 几乎Gross-Pitaevskii状态下二维吸引玻色气体Hartree理论的推导

IF 2.3 1区数学 Q1 MATHEMATICS

Journal de Mathematiques Pures et Appliquees

Pub Date : 2025-10-01 DOI: 10.1016/j.matpur.2025.103800

Lukas Junge , François L.A. Visconti

We study the ground state energy of trapped two-dimensional Bose gases with mean-field type interactions that can be attractive. We prove the stability of second kind of the many-body system and the convergence of the ground state energy per particle to that of a non-linear Schrödinger (NLS) energy functional. Notably, we can take any polynomial scaling of the interaction, and even exponential scalings arbitrarily close to the Gross–Pitaevskii regime, which is a drastic improvement on the best-known result for systems with attractive interactions. As a consequence of the stability of second kind we also obtain Bose–Einstein condensation for the many-body ground states for a much improved range of the diluteness parameter.

我们研究了具有平均场相互作用的二维玻色气体的基态能量。我们证明了第二类多体系统的稳定性和每粒子的基态能量收敛于非线性Schrödinger （NLS）能量泛函。值得注意的是，我们可以对相互作用进行任何多项式缩放，甚至可以任意接近Gross-Pitaevskii状态的指数缩放，这是对具有吸引相互作用的系统的最著名结果的巨大改进。由于第二类的稳定性，我们还获得了多体基态的玻色-爱因斯坦凝聚，其稀释度参数的范围大大提高。

引用次数: 0

Qualitative properties of the spreading speed of a population structured in space and in phenotype 一个种群在空间和表型结构上传播速度的定性性质

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.2025.103804

Nathanaël Boutillon

We consider a nonlocal Fisher-KPP equation that models a population structured in space and in phenotype. The population lives in a heterogeneous periodic environment: the diffusion coefficient, the mutation coefficient and the fitness of an individual may depend on its spatial position and on its phenotype.

We first prove a Freidlin-Gärtner formula for the spreading speed of the population. We then study the behaviour of the spreading speed in different scaling limits (small and large period, small and large mutation coefficient). Finally, we exhibit new phenomena arising thanks to the phenotypic dimension.

Our results are also valid when the phenotype is seen as another spatial variable along which the population does not spread.

我们考虑一个非局部Fisher-KPP方程，该方程模拟了在空间和表型上结构的种群。种群生活在异质周期性环境中：个体的扩散系数、突变系数和适合度可能取决于其空间位置和表型。我们首先证明了人口扩散速度的Freidlin-Gärtner公式。然后，我们研究了不同尺度极限（小周期和大周期，小突变系数和大突变系数）下的传播速度行为。最后，我们展示了由于表型维度而产生的新现象。当表型被视为另一个空间变量时，我们的结果也是有效的，种群不会沿着这个空间变量传播。

引用次数: 0

Long time classical solutions of quasilinear Klein-Gordon equations with small weakly decaying initial data 具有弱衰减小初始数据的拟线性Klein-Gordon方程的长时间经典解

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.2025.103803

Fei Hou , Huicheng Yin

It is well known that for the quasilinear Klein-Gordon equation with quadratic nonlinearity and sufficiently decaying small initial data, there exists a global smooth solution if the space dimensions

d \geq 2

. When the initial data are of size

ε > 0

in the Sobolev space, for the semilinear Klein-Gordon equation satisfying the null condition, the authors in the article (Delort and Fang, 2000 [11]) prove that the solution exists in time

[0, T_{ε})

with

T_{ε} \geq C e^{C ε^{- μ}}

(

μ = 1

d \geq 3

μ = 2 / 3

d = 2

). In the present paper, we will focus on the general quasilinear Klein-Gordon equation without the null condition and further show that the existence time of the solution can be improved to

T_{ε} = + \infty

d \geq 3

and

T_{ε} \geq e^{C ε^{- 2}}

d = 2

. In addition, for

d = 2

and any fixed number

α > 0

, if the weighted

L^{2}

norm of the initial data with the weight

{(1 + | x |)}^{α}

is small, then the solution exists globally and scatters to a free solution. Our arguments are based on the introduction of a new good unknown, the Strichartz estimate, the weighted

L^{2}

-norm estimate and the resonance analysis.

众所周知，对于具有二次非线性和充分衰减的小初始数据的拟线性Klein-Gordon方程，当空间维数d≥2时，存在全局光滑解。在Sobolev空间中，当初始数据大小为ε>；0时，对于满足零条件的半线性Klein-Gordon方程，本文（Delort and Fang, 2000[11]）证明了解在时间[0，t)上存在，且t≥cee ε−μ（当d≥3时μ=1，当d=2时μ=2/3）。本文将重点讨论不带零条件的一般拟线性Klein-Gordon方程，并进一步证明当d≥3时，解的存在时间可提高到Tε=+∞，当d=2时，解的存在时间可提高到Tε≥eCε−2。另外，对于d=2和任意固定数α>；0，如果初始数据的权重为(1+|x|)α的加权L2范数较小，则该解全局存在并散射到一个自由解。我们的论点是基于引入一个新的好未知数、Strichartz估计、加权l2 -范数估计和共振分析。

{"title":"Long time classical solutions of quasilinear Klein-Gordon equations with small weakly decaying initial data","authors":"Fei Hou , Huicheng Yin","doi":"10.1016/j.matpur.2025.103803","DOIUrl":"10.1016/j.matpur.2025.103803","url":null,"abstract":"<div><div>It is well known that for the quasilinear Klein-Gordon equation with quadratic nonlinearity and sufficiently decaying small initial data, there exists a global smooth solution if the space dimensions <span><math><mi>d</mi><mo>≥</mo><mn>2</mn></math></span>. When the initial data are of size <span><math><mi>ε</mi><mo>></mo><mn>0</mn></math></span> in the Sobolev space, for the semilinear Klein-Gordon equation satisfying the null condition, the authors in the article (Delort and Fang, 2000 <span><span>[11]</span></span>) prove that the solution exists in time <span><math><mo>[</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>ε</mi></mrow></msub><mo>)</mo></math></span> with <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>ε</mi></mrow></msub><mo>≥</mo><mi>C</mi><msup><mrow><mi>e</mi></mrow><mrow><mi>C</mi><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mi>μ</mi></mrow></msup></mrow></msup></math></span> (<span><math><mi>μ</mi><mo>=</mo><mn>1</mn></math></span> if <span><math><mi>d</mi><mo>≥</mo><mn>3</mn></math></span>, <span><math><mi>μ</mi><mo>=</mo><mn>2</mn><mo>/</mo><mn>3</mn></math></span> if <span><math><mi>d</mi><mo>=</mo><mn>2</mn></math></span>). In the present paper, we will focus on the general quasilinear Klein-Gordon equation without the null condition and further show that the existence time of the solution can be improved to <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>ε</mi></mrow></msub><mo>=</mo><mo>+</mo><mo>∞</mo></math></span> if <span><math><mi>d</mi><mo>≥</mo><mn>3</mn></math></span> and <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>ε</mi></mrow></msub><mo>≥</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>C</mi><msup><mrow><mi>ε</mi></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></msup></math></span> if <span><math><mi>d</mi><mo>=</mo><mn>2</mn></math></span>. In addition, for <span><math><mi>d</mi><mo>=</mo><mn>2</mn></math></span> and any fixed number <span><math><mi>α</mi><mo>></mo><mn>0</mn></math></span>, if the weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm of the initial data with the weight <span><math><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mo>|</mo><mi>x</mi><mo>|</mo><mo>)</mo></mrow><mrow><mi>α</mi></mrow></msup></math></span> is small, then the solution exists globally and scatters to a free solution. Our arguments are based on the introduction of a new good unknown, the Strichartz estimate, the weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm estimate and the resonance analysis.</div></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"205 ","pages":"Article 103803"},"PeriodicalIF":2.3,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145219207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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