发布求助
文献互助 智能选刊 最新文献

Archive for Rational Mechanics and Analysis最新文献

筛选
英文 中文
Instability and Spectrum of the Linearized Two-Phase Fluids Interface Problem at Shear Flows 剪切流下线性化两相流体界面问题的不稳定性和频谱
IF 2.5 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2024-08-28 DOI: 10.1007/s00205-024-02024-5
Xiao Liu
{"title":"Instability and Spectrum of the Linearized Two-Phase Fluids Interface Problem at Shear Flows","authors":"Xiao Liu","doi":"10.1007/s00205-024-02024-5","DOIUrl":"https://doi.org/10.1007/s00205-024-02024-5","url":null,"abstract":"<p>This paper is concerned with the 2-dim two-phase interface Euler equation linearized at a pair of monotone shear flows in both fluids. We extend the Howard’s Semicircle Theorem and study the eigenvalue distribution of the linearized Euler system. Under certain conditions, there are exactly two eigenvalues for each fixed wave number <span>(kin mathbb {R})</span> in the whole complex plane. We provide sufficient conditions for spectral instability arising from some boundary values of the shear flow velocity. A typical mode is the ocean-air system in which the density ratio of the fluids is sufficiently small. We give a complete picture of eigenvalue distribution for a certain class of shear flows in the ocean-air system.</p>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180060","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}
引用次数: 0
Matrix Displacement Convexity Along Density Flows 沿密度流的矩阵位移凸度
IF 2.5 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2024-08-27 DOI: 10.1007/s00205-024-02021-8
Yair Shenfeld
{"title":"Matrix Displacement Convexity Along Density Flows","authors":"Yair Shenfeld","doi":"10.1007/s00205-024-02021-8","DOIUrl":"https://doi.org/10.1007/s00205-024-02021-8","url":null,"abstract":"<p>A new notion of displacement convexity on a matrix level is developed for density flows arising from mean-field games, compressible Euler equations, entropic interpolation, and semi-classical limits of non-linear Schrödinger equations. Matrix displacement convexity is stronger than the classical notions of displacement convexity, and its verification (formal and rigorous) relies on matrix differential inequalities along the density flows. The matrical nature of these differential inequalities upgrades dimensional functional inequalities to their intrinsic dimensional counterparts, thus improving on many classical results. Applications include turnpike properties, evolution variational inequalities, and entropy growth bounds, which capture the behavior of the density flows along different directions in space.</p>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180061","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}
引用次数: 0
Local Well-Posedness of the Capillary-Gravity Water Waves with Acute Contact Angles 具有锐接触角的毛细管-重力水波的局部良好假设性
IF 2.5 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2024-08-26 DOI: 10.1007/s00205-024-02019-2
Mei Ming, Chao Wang
{"title":"Local Well-Posedness of the Capillary-Gravity Water Waves with Acute Contact Angles","authors":"Mei Ming, Chao Wang","doi":"10.1007/s00205-024-02019-2","DOIUrl":"https://doi.org/10.1007/s00205-024-02019-2","url":null,"abstract":"<p>We consider the two-dimensional capillary-gravity water waves problem where the free surface <span>(Gamma _t)</span> intersects the bottom <span>(Gamma _b)</span> at two contact points. In our previous works (Ming and Wang in SIAM J Math Anal 52(5):4861–4899; Commun Pure Appl Math 74(2), 225–285, 2021), the local well-posedness for this problem has been proved with the contact angles less than <span>(pi /16)</span>. In this paper, we study the case where the contact angles belong to <span>((0, pi /2))</span>. It involves much worse singularities generated from corresponding elliptic systems, which have this strong influence on the regularities for the free surface and the velocity field. Combining the theory of singularity decompositions for elliptic problems with the structure of the water waves system, we obtain a priori energy estimates. Based on these estimates, we also prove the local well-posedness of the solutions in a geometric formulation.</p>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180062","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}
引用次数: 0
A PDE Approach to the Existence and Regularity of Surfaces of Minimum Mean Curvature Variation 最小均方差曲面的存在性和规则性的 PDE 方法
IF 2.5 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2024-08-05 DOI: 10.1007/s00205-024-02016-5
Luis A. Caffarelli, Pablo Raúl Stinga, Hernán Vivas
{"title":"A PDE Approach to the Existence and Regularity of Surfaces of Minimum Mean Curvature Variation","authors":"Luis A. Caffarelli, Pablo Raúl Stinga, Hernán Vivas","doi":"10.1007/s00205-024-02016-5","DOIUrl":"https://doi.org/10.1007/s00205-024-02016-5","url":null,"abstract":"<p>We develop an analytic theory of existence and regularity of surfaces (given by graphs) arising from the geometric minimization problem </p><span>$$begin{aligned} min _mathcal {M}frac{1}{2}int _mathcal {M}|nabla _{mathcal {M}}H|^2,{text {d}}A, end{aligned}$$</span><p>where <span>(mathcal {M})</span> ranges over all <i>n</i>-dimensional manifolds in <span>(mathbb {R}^{n+1})</span> with a prescribed boundary, <span>(nabla _{mathcal {M}}H)</span> is the tangential gradient along <span>(mathcal {M})</span> of the mean curvature <i>H</i> of <span>(mathcal {M})</span> and d<i>A</i> is the differential of surface area. The minimizers, called surfaces of minimum mean curvature variation, are central in applications of computer-aided design, computer-aided manufacturing and mechanics. Our main results show the existence of both smooth surfaces and of variational solutions to the minimization problem together with geometric regularity results in the case of graphs. These are the first analytic results available for this problem.</p>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945709","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}
引用次数: 0
Quantified Legendreness and the Regularity of Minima 量化传奇和最小值的规律性
IF 2.5 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2024-07-29 DOI: 10.1007/s00205-024-02008-5
Cristiana De Filippis, Lukas Koch, Jan Kristensen
{"title":"Quantified Legendreness and the Regularity of Minima","authors":"Cristiana De Filippis, Lukas Koch, Jan Kristensen","doi":"10.1007/s00205-024-02008-5","DOIUrl":"https://doi.org/10.1007/s00205-024-02008-5","url":null,"abstract":"<p>We introduce a new quantification of nonuniform ellipticity in variational problems via convex duality, and prove higher differentiability and 2<i>d</i>-smoothness results for vector valued minimizers of possibly degenerate functionals. Our framework covers convex, anisotropic polynomials as prototypical model examples—in particular, we improve in an essentially optimal fashion Marcellini’s original results (Marcellini in Arch Rat Mech Anal 105:267–284, 1989).\u0000</p>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141869739","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}
引用次数: 0
The Gradient Flow for Entropy on Closed Planar Curves 封闭平面曲线上的熵梯度流
IF 2.5 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2024-07-27 DOI: 10.1007/s00205-024-02014-7
Lachlann O’Donnell, Glen Wheeler, Valentina-Mira Wheeler
{"title":"The Gradient Flow for Entropy on Closed Planar Curves","authors":"Lachlann O’Donnell, Glen Wheeler, Valentina-Mira Wheeler","doi":"10.1007/s00205-024-02014-7","DOIUrl":"https://doi.org/10.1007/s00205-024-02014-7","url":null,"abstract":"<p>In this paper we consider the steepest descent <span>(L^2)</span>-gradient flow of the entropy functional. The flow expands convex curves, with the radius of an initial circle growing like the square root of time. Our main result is that, for any initial curve (either immersed locally strictly convex of class <span>(C^2)</span> or embedded of class <span>(W^{2,2})</span> bounding a strictly convex body), the flow converges smoothly to a round expanding multiply-covered circle.</p>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141773753","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}
引用次数: 0
Interior Regularity for Two-Dimensional Stationary Q-Valued Maps 二维静态 Q 值映射的内部正则性
IF 2.5 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2024-07-22 DOI: 10.1007/s00205-024-02011-w
Jonas Hirsch, Luca Spolaor
{"title":"Interior Regularity for Two-Dimensional Stationary Q-Valued Maps","authors":"Jonas Hirsch, Luca Spolaor","doi":"10.1007/s00205-024-02011-w","DOIUrl":"https://doi.org/10.1007/s00205-024-02011-w","url":null,"abstract":"<p>We prove that 2-dimensional <i>Q</i>-valued maps that are stationary with respect to outer and inner variations of the Dirichlet energy are Hölder continuous and that the dimension of their singular set is at most one. In the course of the proof we establish a strong concentration-compactness theorem for equicontinuous maps that are stationary with respect to outer variations only, and which holds in every dimensions.</p>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743615","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}
引用次数: 0
Objective Rates as Covariant Derivatives on the Manifold of Riemannian Metrics 作为黎曼度量漫域上协变导数的客观率
IF 2.5 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2024-07-15 DOI: 10.1007/s00205-024-02010-x
B. Kolev, R. Desmorat
{"title":"Objective Rates as Covariant Derivatives on the Manifold of Riemannian Metrics","authors":"B. Kolev, R. Desmorat","doi":"10.1007/s00205-024-02010-x","DOIUrl":"https://doi.org/10.1007/s00205-024-02010-x","url":null,"abstract":"<p>The subject of so-called objective derivatives in Continuum Mechanics has a long history and has generated varying views concerning their true mathematical interpretation. Several attempts have been made to provide a mathematical definition that would at least partially unify the existing notions. In this paper, we demonstrate that, under natural assumptions, all objective derivatives correspond to covariant derivatives on the infinite-dimensional manifold <span>(textrm{Met}(mathcal {B}))</span> of Riemannian metrics on the body. Furthermore, a natural Leibniz rule enables canonical extensions from covariant to contravariant tensor fields and vice versa. This makes the sometimes-used distinction between objective derivatives of “Lie type” and “co-rotational type” unnecessary. For an exhaustive list of objective derivatives found in the literature, we exhibit the corresponding covariant derivative on <span>(textrm{Met}(mathcal {B}))</span>.</p>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141721976","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}
引用次数: 0
Degeneration of 7-Dimensional Minimal Hypersurfaces Which are Stable or Have a Bounded Index 稳定或指数受限的 7 维最小超曲面的退化
IF 2.5 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2024-07-03 DOI: 10.1007/s00205-024-02003-w
Nick Edelen
{"title":"Degeneration of 7-Dimensional Minimal Hypersurfaces Which are Stable or Have a Bounded Index","authors":"Nick Edelen","doi":"10.1007/s00205-024-02003-w","DOIUrl":"https://doi.org/10.1007/s00205-024-02003-w","url":null,"abstract":"<p>A 7-dimensional area-minimizing embedded hypersurface <span>(M^7)</span> will in general have a discrete singular set, and the same is true if <i>M</i> is locally stable provided <span>({mathcal {H}}^6(textrm{sing}M) = 0)</span>. We show that if <span>(M_i^7)</span> is a sequence of 7D minimal hypersurfaces which are minimizing, stable, or have bounded index, then <span>(M_i rightarrow M)</span> can limit to a singular <span>(M^7)</span> with only very controlled geometry, topology, and singular set. We show that one can always “parameterize” a subsequence <span>(i')</span> with controlled bi-Lipschitz maps <span>(phi _{i'})</span> taking <span>(phi _{i'}(M_{1'}) = M_{i'})</span>. As a consequence, we prove the space of smooth, closed, embedded minimal hypersurfaces <i>M</i> in a closed Riemannian 8-manifold <span>((N^8, g))</span> with a priori bounds <span>({mathcal {H}}^7(M) leqq Lambda )</span> and <span>(textrm{index}(M) leqq I)</span> divides into finitely-many diffeomorphism types, and this finiteness continues to hold if one allows the metric <i>g</i> to vary, or <i>M</i> to be singular.</p>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551825","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}
引用次数: 0
Stable Recovery of Coefficients in an Inverse Fault Friction Problem 反断层摩擦问题中系数的稳定恢复
IF 2.5 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2024-07-01 DOI: 10.1007/s00205-024-02009-4
Maarten V. de Hoop, Matti Lassas, Jinpeng Lu, Lauri Oksanen
{"title":"Stable Recovery of Coefficients in an Inverse Fault Friction Problem","authors":"Maarten V. de Hoop, Matti Lassas, Jinpeng Lu, Lauri Oksanen","doi":"10.1007/s00205-024-02009-4","DOIUrl":"https://doi.org/10.1007/s00205-024-02009-4","url":null,"abstract":"<p>We consider the inverse fault friction problem of determining the friction coefficient in the Tresca friction model, which can be formulated as an inverse problem for differential inequalities. We show that the measurements of elastic waves during a rupture uniquely determine the friction coefficient at the rupture surface with explicit stability estimates.</p>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508634","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}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信