Archive for Rational Mechanics and Analysis最新文献_第8页

A Limit of Nonplanar 5-Body Central Configurations is Nonplanar 非平面五体中心构型的非平面极限

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-01-31 DOI: 10.1007/s00205-023-01949-7

Alain Albouy, Antonio Carlos Fernandes

引用次数: 0

Intermittency and Lower Dimensional Dissipation in Incompressible Fluids 不可压缩流体中的间歇性和低维耗散

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-01-25 DOI: 10.1007/s00205-023-01954-w

Luigi De Rosa, Philip Isett

{"title":"Intermittency and Lower Dimensional Dissipation in Incompressible Fluids","authors":"Luigi De Rosa, Philip Isett","doi":"10.1007/s00205-023-01954-w","DOIUrl":"https://doi.org/10.1007/s00205-023-01954-w","url":null,"abstract":"In the context of incompressible fluids, the observation that turbulent singular structures fail to be space filling is known as “intermittency”, and it has strong experimental foundations. Consequently, as first pointed out by Landau, real turbulent flows do not satisfy the central assumptions of homogeneity and self-similarity in the K41 theory, and the K41 prediction of structure function exponents (zeta _p={p}/{3}) might be inaccurate. In this work we prove that, in the inviscid case, energy dissipation that is lower-dimensional in an appropriate sense implies deviations from the K41 prediction in every p-th order structure function for (p>3). By exploiting a Lagrangian-type Minkowski dimension that is very reminiscent of the Taylor’s frozen turbulence hypothesis, our strongest upper bound on (zeta _p) coincides with the (beta )-model proposed by Frisch, Sulem and Nelkin in the late 70s, adding some rigorous analytical foundations to the model. More generally, we explore the relationship between dimensionality assumptions on the dissipation support and restrictions on the p-th order absolute structure functions. This approach differs from the current mathematical works on intermittency by its focus on geometrical rather than purely analytical assumptions. The proof is based on a new local variant of the celebrated Constantin-E-Titi argument that features the use of a third order commutator estimate, the special double regularity of the pressure, and mollification along the flow of a vector field.","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139589947","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 BPHZ Theorem for Regularity Structures via the Spectral Gap Inequality 通过谱差距不等式实现规则性结构的 BPHZ 定理

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-01-23 DOI: 10.1007/s00205-023-01946-w

Martin Hairer, Rhys Steele

引用次数: 0

Stability and Cascades for the Kolmogorov–Zakharov Spectrum of Wave Turbulence 波湍流的科尔莫戈罗夫-扎哈罗夫频谱的稳定性和级联性

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-01-23 DOI: 10.1007/s00205-023-01953-x

Charles Collot, Helge Dietert, Pierre Germain

引用次数: 0

Weak Solutions of Mullins–Sekerka Flow as a Hilbert Space Gradient Flow 作为希尔伯特空间梯度流的穆林斯-塞克尔卡流的弱解

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-01-23 DOI: 10.1007/s00205-023-01950-0

{"title":"Weak Solutions of Mullins–Sekerka Flow as a Hilbert Space Gradient Flow","authors":"","doi":"10.1007/s00205-023-01950-0","DOIUrl":"https://doi.org/10.1007/s00205-023-01950-0","url":null,"abstract":"<h3>Abstract</h3> We propose a novel weak solution theory for the Mullins–Sekerka equation in dimensions (d=2) and 3, primarily motivated from a gradient flow perspective. Previous existence results on weak solutions due to Luckhaus and Sturzenhecker (Calc. Var. PDE 3, 1995) or Röger (SIAM J. Math. Anal. 37, 2005) left open the inclusion of both a sharp energy dissipation principle and a weak formulation of the contact angle at the intersection of the interface and the domain boundary. To incorporate these, we introduce a functional framework encoding a weak solution concept for Mullins–Sekerka flow essentially relying only on (i) a single sharp energy dissipation inequality in the spirit of De Giorgi, and (ii) a weak formulation for an arbitrary fixed contact angle through a distributional representation of the first variation of the underlying capillary energy. Both ingredients are intrinsic to the interface of the evolving phase indicator and an explicit distributional PDE formulation with potentials can be derived from them. The existence of weak solutions is established via subsequential limit points of the naturally associated minimizing movements scheme. Smooth solutions are consistent with the classical Mullins–Sekerka flow, and even further, we expect our solution concept to be amenable, at least in principle, to the recently developed relative entropy approach for curvature driven interface evolution.","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139560886","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

Microscopic Derivation of a Traffic Flow Model with a Bifurcation 带有分岔的交通流模型的微观推导

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-01-19 DOI: 10.1007/s00205-023-01948-8

P. Cardaliaguet, N. Forcadel

引用次数: 0

Traveling Wave Solutions to the One-Phase Muskat Problem: Existence and Stability 单相穆斯卡特问题的行波解：存在性与稳定性

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-01-18 DOI: 10.1007/s00205-023-01951-z

Huy Q. Nguyen, Ian Tice

引用次数: 0

Stable Singularity Formation for the Keller–Segel System in Three Dimensions 三维凯勒-西格尔系统的稳定奇点形成

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-01-05 DOI: 10.1007/s00205-023-01947-9

Irfan Glogić, Birgit Schörkhuber

{"title":"Stable Singularity Formation for the Keller–Segel System in Three Dimensions","authors":"Irfan Glogić, Birgit Schörkhuber","doi":"10.1007/s00205-023-01947-9","DOIUrl":"10.1007/s00205-023-01947-9","url":null,"abstract":"<div>We consider the parabolic–elliptic Keller–Segel system in dimensions (d geqq 3), which is the mass supercritical case. This system is known to exhibit rich dynamical behavior including singularity formation via self-similar solutions. An explicit example was found more than two decades ago by Brenner et al. (Nonlinearity 12(4):1071–1098, 1999), and is conjectured to be nonlinearly radially stable. We prove this conjecture for (d=3). Our approach consists of reformulating the problem in similarity variables and studying the Cauchy evolution in intersection Sobolev spaces via semigroup theory methods. To solve the underlying spectral problem, we use a technique we recently established in Glogić and Schörkhuber (Comm Part Differ Equ 45(8):887–912, 2020). To the best of our knowledge, this provides the first result on stable self-similar blowup for the Keller–Segel system. Furthermore, the extension of our result to any higher dimension is straightforward. We point out that our approach is general and robust, and can therefore be applied to a wide class of parabolic models.</div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-023-01947-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139111895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Local Well-Posedness of the Skew Mean Curvature Flow for Small Data in d≧2 Dimensions. d≧2维小数据斜均值曲率流的局部拟合优度

IF 2.5 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-01-01 Epub Date: 2024-01-25 DOI: 10.1007/s00205-023-01952-y

Jiaxi Huang, Daniel Tataru

{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">Local Well-Posedness of the Skew Mean Curvature Flow for Small Data in <ns0:math><ns0:mrow><ns0:mi>d</ns0:mi><ns0:mo>≧</ns0:mo><ns0:mn>2</ns0:mn></ns0:mrow></ns0:math> Dimensions.","authors":"Jiaxi Huang, Daniel Tataru","doi":"10.1007/s00205-023-01952-y","DOIUrl":"10.1007/s00205-023-01952-y","url":null,"abstract":"The skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in <math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>2</mn></mrow></msup></math> (or more generally, in a Riemannian manifold). It can be viewed as a Schrödinger analogue of the mean curvature flow, or alternatively as a quasilinear version of the Schrödinger Map equation. In an earlier paper, the authors introduced a harmonic/Coulomb gauge formulation of the problem, and used it to prove small data local well-posedness in dimensions <math><mrow><mi>d</mi><mo>≧</mo><mn>4</mn></mrow></math>. In this article, we prove small data local well-posedness in low-regularity Sobolev spaces for the skew mean curvature flow in dimension <math><mrow><mi>d</mi><mo>≧</mo><mn>2</mn></mrow></math>. This is achieved by introducing a new, heat gauge formulation of the equations, which turns out to be more robust in low dimensions.","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10811054/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139572307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Approximation of Classical Two-Phase Flows of Viscous Incompressible Fluids by a Navier-Stokes/Allen-Cahn System. 纳维-斯托克斯/阿伦-卡恩系统对粘性不可压缩流体经典两相流的近似。

IF 2.6 1区数学

Archive for Rational Mechanics and Analysis Pub Date : 2024-01-01 Epub Date: 2024-09-03 DOI: 10.1007/s00205-024-02020-9

Helmut Abels, Julian Fischer, Maximilian Moser

{"title":"Approximation of Classical Two-Phase Flows of Viscous Incompressible Fluids by a Navier-Stokes/Allen-Cahn System.","authors":"Helmut Abels, Julian Fischer, Maximilian Moser","doi":"10.1007/s00205-024-02020-9","DOIUrl":"https://doi.org/10.1007/s00205-024-02020-9","url":null,"abstract":"We show convergence of the Navier-Stokes/Allen-Cahn system to a classical sharp interface model for the two-phase flow of two viscous incompressible fluids with same viscosities in a smooth bounded domain in two and three space dimensions as long as a smooth solution of the limit system exists. Moreover, we obtain error estimates with the aid of a relative entropy method. Our results hold provided that the mobility <math> <mrow><msub><mi>m</mi> <mi>ε</mi></msub> <mo>></mo> <mn>0</mn></mrow> </math> in the Allen-Cahn equation tends to zero in a subcritical way, i.e., <math> <mrow><msub><mi>m</mi> <mi>ε</mi></msub> <mo>=</mo> <msub><mi>m</mi> <mn>0</mn></msub> <msup><mi>ε</mi> <mi>β</mi></msup> </mrow> </math> for some <math><mrow><mi>β</mi> <mo>∈</mo> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mo>)</mo></mrow> </math> and <math> <mrow><msub><mi>m</mi> <mn>0</mn></msub> <mo>></mo> <mn>0</mn></mrow> </math> . The proof proceeds by showing via a relative entropy argument that the solution to the Navier-Stokes/Allen-Cahn system remains close to the solution of a perturbed version of the two-phase flow problem, augmented by an extra mean curvature flow term <math> <mrow><msub><mi>m</mi> <mi>ε</mi></msub> <msub><mi>H</mi> <msub><mi>Γ</mi> <mi>t</mi></msub> </msub> </mrow> </math> in the interface motion. In a second step, it is easy to see that the solution to the perturbed problem is close to the original two-phase flow.","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11371890/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142141788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0