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Communications in Partial Differential Equations最新文献

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Partial regularity of the heat flow of half-harmonic maps and applications to harmonic maps with free boundary 半调和图热流的部分正则性及其在自由边界调和图中的应用
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-11-28 DOI: 10.1080/03605302.2022.2091453
A. Hyder, A. Segatti, Y. Sire, Changyou Wang
{"title":"Partial regularity of the heat flow of half-harmonic maps and applications to harmonic maps with free boundary","authors":"A. Hyder, A. Segatti, Y. Sire, Changyou Wang","doi":"10.1080/03605302.2022.2091453","DOIUrl":"https://doi.org/10.1080/03605302.2022.2091453","url":null,"abstract":"Abstract We introduce a heat flow associated to half-harmonic maps, which have been introduced by Da Lio and Rivière. Those maps exhibit integrability by compensation in one space dimension and are related to harmonic maps with free boundary. We consider a new flow associated to these harmonic maps with free boundary which is actually motivated by a rather unusual heat flow for half-harmonic maps. We construct then weak solutions and prove their partial regularity in space and time via a Ginzburg-Landau approximation. The present paper complements the study initiated by Struwe and Chen-Lin.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"47 1","pages":"1845 - 1882"},"PeriodicalIF":1.9,"publicationDate":"2021-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47651817","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: 7
Quantum entanglement and the growth of Laplacian eigenfunctions 量子纠缠和拉普拉斯本征函数的增长
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-11-24 DOI: 10.1080/03605302.2023.2175217
S. Steinerberger
{"title":"Quantum entanglement and the growth of Laplacian eigenfunctions","authors":"S. Steinerberger","doi":"10.1080/03605302.2023.2175217","DOIUrl":"https://doi.org/10.1080/03605302.2023.2175217","url":null,"abstract":"Abstract We study the growth of Laplacian eigenfunctions on compact manifolds (M, g). Hörmander proved sharp polynomial bounds on which are attained on the sphere. On a “generic” manifold, the behavior seems to be different: both numerics and Berry’s random wave model suggest as the typical behavior. We propose a mechanism, centered around an analog of the spectral projector, for explaining the slow growth in the generic case: for to be large, it is necessary that either (1) several of the first n eigenfunctions were large in x 0 or (2) that is strongly correlated with a suitable linear combination of the first n eigenfunctions on most of the manifold or (3) both. An interesting byproduct is quantum entanglement for Laplacian eigenfunctions: the existence of two distinct points such that the sequences and do not behave like independent random variables. The existence of such points is not to be expected for generic manifolds but common for the classical manifolds and subtly intertwined with eigenfunction concentration.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"48 1","pages":"511 - 541"},"PeriodicalIF":1.9,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43836263","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: 3
The Yang-Mills heat flow with random distributional initial data 初始数据随机分布的Yang-Mills热流
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-11-20 DOI: 10.1080/03605302.2023.2169937
Sky Cao, S. Chatterjee
{"title":"The Yang-Mills heat flow with random distributional initial data","authors":"Sky Cao, S. Chatterjee","doi":"10.1080/03605302.2023.2169937","DOIUrl":"https://doi.org/10.1080/03605302.2023.2169937","url":null,"abstract":"Abstract We construct local solutions to the Yang–Mills heat flow (in the DeTurck gauge) for a certain class of random distributional initial data, which includes the 3D Gaussian free field. The main idea, which goes back to work of Bourgain as well as work of Da Prato–Debussche, is to decompose the solution into a rougher linear part and a smoother nonlinear part, and to control the latter by probabilistic arguments. In a companion work, we use the main results of this paper to propose a way toward the construction of 3D Yang–Mills measures.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"48 1","pages":"209 - 251"},"PeriodicalIF":1.9,"publicationDate":"2021-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44725470","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: 6
Spectral asymptotics for the vectorial damped wave equation 矢量阻尼波动方程的谱渐近性
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-11-17 DOI: 10.1080/03605302.2022.2137678
Guillaume Klein
{"title":"Spectral asymptotics for the vectorial damped wave equation","authors":"Guillaume Klein","doi":"10.1080/03605302.2022.2137678","DOIUrl":"https://doi.org/10.1080/03605302.2022.2137678","url":null,"abstract":"Abstract The eigenfrequencies associated to a scalar damped wave equation are known to belong to a band parallel to the real axis. Sjöstrand showed that up to a set of density 0, the eigenfrequencies are confined in a thinner band determined by the Birkhoff limits of the damping term. In this article we show that this result is still true for a vectorial damped wave equation. In this setting the Lyapunov exponents of the cocycle given by the damping term play the role of the Birkhoff limits of the scalar setting.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"48 1","pages":"1 - 21"},"PeriodicalIF":1.9,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47909859","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
Existence and decay of traveling waves for the nonlocal Gross–Pitaevskii equation 非局部Gross–Pitaevskii方程行波的存在性和衰减性
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-11-10 DOI: 10.1080/03605302.2022.2070853
André de Laire, Salvador L'opez-Mart'inez
{"title":"Existence and decay of traveling waves for the nonlocal Gross–Pitaevskii equation","authors":"André de Laire, Salvador L'opez-Mart'inez","doi":"10.1080/03605302.2022.2070853","DOIUrl":"https://doi.org/10.1080/03605302.2022.2070853","url":null,"abstract":"Abstract We consider the nonlocal Gross–Pitaevskii equation that models a Bose gas with general nonlocal interactions between particles in one spatial dimension, with constant density far away. We address the problem of the existence of traveling waves with nonvanishing conditions at infinity, i.e. dark solitons. Under general conditions on the interactions, we prove existence of dark solitons for almost every subsonic speed. Moreover, we show existence in the whole subsonic regime for a family of potentials. The proofs rely on a Mountain Pass argument combined with the so-called “monotonicity trick,” as well as on a priori estimates for the Palais–Smale sequences. Finally, we establish properties of the solitons such as exponential decay at infinity and analyticity.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"47 1","pages":"1732 - 1794"},"PeriodicalIF":1.9,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48840789","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: 2
Stable discontinuous stationary solutions to reaction-diffusion-ODE systems 反应-扩散- ode系统的不连续稳定解
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-11-01 DOI: 10.1080/03605302.2023.2190525
S. Cygan, A. Marciniak-Czochra, G. Karch, Kanako Suzuki
{"title":"Stable discontinuous stationary solutions to reaction-diffusion-ODE systems","authors":"S. Cygan, A. Marciniak-Czochra, G. Karch, Kanako Suzuki","doi":"10.1080/03605302.2023.2190525","DOIUrl":"https://doi.org/10.1080/03605302.2023.2190525","url":null,"abstract":"Abstract A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial boundary value problems may have different types of stationary solutions. In our parallel work [Instability of all regular stationary solutions to reaction-diffusion-ODE systems (2021)], regular (i.e. sufficiently smooth) stationary solutions are shown to exist, however, all of them are unstable. The goal of this work is to construct discontinuous stationary solutions to general reaction-diffusion-ODE systems and to find sufficient conditions for their stability.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"48 1","pages":"478 - 510"},"PeriodicalIF":1.9,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44355220","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: 5
Horizontal magnetic fields and improved Hardy inequalities in the Heisenberg group Heisenberg群中的水平磁场和改进的Hardy不等式
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-10-26 DOI: 10.1080/03605302.2023.2191326
B. Cassano, Valentina Franceschi, D. Krejčiřík, D. Prandi
{"title":"Horizontal magnetic fields and improved Hardy inequalities in the Heisenberg group","authors":"B. Cassano, Valentina Franceschi, D. Krejčiřík, D. Prandi","doi":"10.1080/03605302.2023.2191326","DOIUrl":"https://doi.org/10.1080/03605302.2023.2191326","url":null,"abstract":"Abstract In this article, we introduce a notion of magnetic field in the Heisenberg group and we study its influence on spectral properties of the corresponding magnetic (sub-elliptic) Laplacian. We show that uniform magnetic fields uplift the bottom of the spectrum. For magnetic fields vanishing at infinity, including Aharonov–Bohm potentials, we derive magnetic improvements to a variety of Hardy-type inequalities for the Heisenberg sub-Laplacian. In particular, we establish a sub-Riemannian analogue of Laptev and Weidl sub-criticality result for magnetic Laplacians in the plane. Instrumental for our argument is the validity of a Hardy-type inequality for the Folland–Stein operator, that we prove in this article and has an interest on its own.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"48 1","pages":"711 - 752"},"PeriodicalIF":1.9,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49010097","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: 1
Spectral theory for Maxwell’s equations at the interface of a metamaterial. Part II: Limiting absorption, limiting amplitude principles and interface resonance 超材料界面处麦克斯韦方程组的谱理论。第二部分:限吸、限幅原理及界面共振
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-10-13 DOI: 10.1080/03605302.2022.2051188
M. Cassier, C. Hazard, P. Joly
{"title":"Spectral theory for Maxwell’s equations at the interface of a metamaterial. Part II: Limiting absorption, limiting amplitude principles and interface resonance","authors":"M. Cassier, C. Hazard, P. Joly","doi":"10.1080/03605302.2022.2051188","DOIUrl":"https://doi.org/10.1080/03605302.2022.2051188","url":null,"abstract":"Abstract This paper is concerned with the time-dependent Maxwell’s equations for a plane interface between a negative material described by the Drude model and the vacuum, which fill, respectively, two complementary half-spaces. In a first paper, we have constructed a generalized Fourier transform which diagonalizes the Hamiltonian that represents the propagation of transverse electric waves. In this second paper, we use this transform to prove the limiting absorption and limiting amplitude principles, which concern, respectively, the behavior of the resolvent near the continuous spectrum and the long time response of the medium to a time-harmonic source of prescribed frequency. This paper also underlines the existence of an interface resonance which occurs when there exists a particular frequency characterized by a ratio of permittivities and permeabilities equal to −1 across the interface. At this frequency, the response of the system to a harmonic forcing term blows up linearly in time. Such a resonance is unusual for wave problem in unbounded domains and corresponds to a non-zero embedded eigenvalue of infinite multiplicity of the underlying operator. This is the time counterpart of the ill-posdness of the corresponding harmonic problem.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"47 1","pages":"1217 - 1295"},"PeriodicalIF":1.9,"publicationDate":"2021-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41487394","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: 6
Dissipative structure for symmetric hyperbolic-parabolic systems with Korteweg-type dispersion 具有Korteweg型色散的对称双曲-抛物型系统的耗散结构
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-10-10 DOI: 10.1080/03605302.2021.1983596
S. Kawashima, Y. Shibata, Jiang Xu
{"title":"Dissipative structure for symmetric hyperbolic-parabolic systems with Korteweg-type dispersion","authors":"S. Kawashima, Y. Shibata, Jiang Xu","doi":"10.1080/03605302.2021.1983596","DOIUrl":"https://doi.org/10.1080/03605302.2021.1983596","url":null,"abstract":"Abstract In this paper, we are concerned with generally symmetric hyperbolic-parabolic systems with Korteweg-type dispersion. Referring to those classical efforts by Kawashima et al., we formulate new structural conditions for the Korteweg-type dispersion and develop the dissipative mechanism of “regularity-gain type.” As an application, it is checked that several concrete model systems (e.g., the compressible Navier-Stokes(-Fourier)-Korteweg system) satisfy the general structural conditions. In addition, the optimality of our general theory on the dissipative structure is also verified by calculating the asymptotic expansions of eigenvalues.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"47 1","pages":"378 - 400"},"PeriodicalIF":1.9,"publicationDate":"2021-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44204708","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: 11
Dirichlet problem for weakly harmonic maps with rough data 具有粗糙数据的弱调和映射的Dirichlet问题
IF 1.9 2区 数学
Communications in Partial Differential Equations Pub Date : 2021-10-08 DOI: 10.1080/03605302.2022.2056705
Gael Diebou Yomgne, H. Koch
{"title":"Dirichlet problem for weakly harmonic maps with rough data","authors":"Gael Diebou Yomgne, H. Koch","doi":"10.1080/03605302.2022.2056705","DOIUrl":"https://doi.org/10.1080/03605302.2022.2056705","url":null,"abstract":"Abstract Weakly harmonic maps from a domain (the upper half-space or a bounded domain, ) into a smooth closed manifold are studied. Prescribing small Dirichlet data in either of the classes or we establish solvability of the resulting boundary value problems by means of a nonvariational method. As a by-product, solutions are shown to be locally smooth, Moreover, we show that boundary data can be chosen large in the underlying topologies if Ω is smooth and bounded by perturbing strictly stable smooth harmonic maps.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"47 1","pages":"1504 - 1535"},"PeriodicalIF":1.9,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49070242","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: 3
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