Annals of Pde最新文献_第9页

Sedimentation of random suspensions and the effect of hyperuniformity 随机悬浮液的沉淀和超均匀性的影响

IF 2.8 1区数学

Annals of Pde Pub Date : 2022-01-11 DOI: 10.1007/s40818-021-00115-0

Mitia Duerinckx, Antoine Gloria

{"title":"Sedimentation of random suspensions and the effect of hyperuniformity","authors":"Mitia Duerinckx, Antoine Gloria","doi":"10.1007/s40818-021-00115-0","DOIUrl":"10.1007/s40818-021-00115-0","url":null,"abstract":"<div><p>This work is concerned with the mathematical analysis of the bulk rheology of random suspensions of rigid particles settling under gravity in viscous fluids. Each particle generates a fluid flow that in turn acts on other particles and hinders their settling. In an equilibrium perspective, for a given ensemble of particle positions, we analyze both the associated mean settling speed and the velocity fluctuations of individual particles. In the 1970s, Batchelor gave a proper definition of the mean settling speed, a 60-year-old open problem in physics, based on the appropriate renormalization of long-range particle contributions. In the 1980s, a celebrated formal calculation by Caflisch and Luke suggested that velocity fluctuations in dimension <span>(d=3)</span> should diverge with the size of the sedimentation tank, contradicting both intuition and experimental observations. The role of long-range self-organization of suspended particles in form of hyperuniformity was later put forward to explain additional screening of this divergence in steady-state observations. In the present contribution, we develop the first rigorous theory that allows to justify all these formal calculations of the physics literature.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"8 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2022-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50470902","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: 21

Global Solutions to Multi-dimensional Topological Euler Alignment Systems 多维拓扑Euler对准系统的全局解

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-12-22 DOI: 10.1007/s40818-021-00116-z

Daniel Lear, David N. Reynolds, Roman Shvydkoy

引用次数: 3

Linear stability analysis of the homogeneous Couette flow in a 2D isentropic compressible fluid 二维等熵可压缩流体中均匀Couette流的线性稳定性分析

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-10-19 DOI: 10.1007/s40818-021-00112-3

Paolo Antonelli, Michele Dolce, Pierangelo Marcati

{"title":"Linear stability analysis of the homogeneous Couette flow in a 2D isentropic compressible fluid","authors":"Paolo Antonelli, Michele Dolce, Pierangelo Marcati","doi":"10.1007/s40818-021-00112-3","DOIUrl":"10.1007/s40818-021-00112-3","url":null,"abstract":"<div><p>In this paper, we study the linear stability properties of perturbations around the homogeneous Couette flow for a 2D isentropic compressible fluid in the domain <span>(mathbb {T}times mathbb {R})</span>. In the inviscid case there is a generic Lyapunov type instability for the density and the irrotational component of the velocity field. More precisely, we prove that their <span>(L^2)</span> norm grows as <span>(t^{1/2})</span> and this confirms previous observations in the physics literature. On the contrary, the solenoidal component of the velocity field experiences inviscid damping, namely it decays to zero even in the absence of viscosity. For a viscous compressible fluid, we show that the perturbations may have a transient growth of order <span>(nu ^{-1/6})</span> (with <span>(nu ^{-1})</span> being proportional to the Reynolds number) on a time-scale <span>(nu ^{-1/3})</span>, after which it decays exponentially fast. This phenomenon is also called enhanced dissipation and our result appears to be the first to detect this mechanism for a compressible flow, where an exponential decay for the density is not a priori trivial given the absence of dissipation in the continuity equation.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"7 2","pages":""},"PeriodicalIF":2.8,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-021-00112-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50497360","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: 14

Stability of Transonic Contact Discontinuity for Two-Dimensional Steady Compressible Euler Flows in a Finitely Long Nozzle 有限长喷管内二维定常可压缩Euler流的跨声速接触间断稳定性

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-09-23 DOI: 10.1007/s40818-021-00113-2

Feimin Huang, Jie Kuang, Dehua Wang, Wei Xiang

{"title":"Stability of Transonic Contact Discontinuity for Two-Dimensional Steady Compressible Euler Flows in a Finitely Long Nozzle","authors":"Feimin Huang, Jie Kuang, Dehua Wang, Wei Xiang","doi":"10.1007/s40818-021-00113-2","DOIUrl":"10.1007/s40818-021-00113-2","url":null,"abstract":"<div><p>We consider the stability of transonic contact discontinuity for the two-dimensional steady compressible Euler flows in a finitely long nozzle. This is the first work on the mixed-type problem of transonic flows across a contact discontinuity as a free boundary in nozzles. We start with the Euler-Lagrangian transformation to straighten the contact discontinuity in the new coordinates. However, the upper nozzle wall in the subsonic region depending on the mass flux becomes a free boundary after the transformation. Then we develop new ideas and techniques to solve the free-boundary problem in three steps: (1) we fix the free boundary and generate a new iteration scheme to solve the corresponding fixed boundary value problem of the hyperbolic-elliptic mixed type by building some powerful estimates for both the first-order hyperbolic equation and a second-order nonlinear elliptic equation in a Lipschitz domain; (2) we update the new free boundary by constructing a mapping that has a fixed point; (3) we establish via the inverse Lagrangian coordinate transformation that the original free interface problem admits a unique piecewise smooth transonic solution near the background state, which consists of a smooth subsonic flow and a smooth supersonic flow with a contact discontinuity.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"7 2","pages":""},"PeriodicalIF":2.8,"publicationDate":"2021-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-021-00113-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50509261","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: 7

Incompressible Euler Limit from Boltzmann Equation with Diffuse Boundary Condition for Analytic Data 具有扩散边界条件的Boltzmann方程的不可压缩Euler极限

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-08-27 DOI: 10.1007/s40818-021-00108-z

Juhi Jang, Chanwoo Kim

{"title":"Incompressible Euler Limit from Boltzmann Equation with Diffuse Boundary Condition for Analytic Data","authors":"Juhi Jang, Chanwoo Kim","doi":"10.1007/s40818-021-00108-z","DOIUrl":"10.1007/s40818-021-00108-z","url":null,"abstract":"<div><p>A rigorous derivation of the incompressible Euler equations with the no-penetration boundary condition from the Boltzmann equation with the diffuse reflection boundary condition has been a challenging open problem. We settle this open question in the affirmative when the initial data of fluid are well-prepared in a real analytic space, in 3D half space. As a key of this advance, we capture the Navier-Stokes equations of </p><div><div><span>$$begin{aligned} textit{viscosity} sim frac{textit{Knudsen number}}{textit{Mach number}} end{aligned}$$</span></div></div><p>satisfying the no-slip boundary condition, as an <i>intermediary</i> approximation of the Euler equations through a new Hilbert-type expansion of the Boltzmann equation with the diffuse reflection boundary condition. Aiming to justify the approximation we establish a novel quantitative <span>(L^p)</span>-<span>(L^infty )</span> estimate of the Boltzmann perturbation around a local Maxwellian of such viscous approximation, along with the commutator estimates and the integrability gain of the hydrodynamic part in various spaces; we also establish direct estimates of the Navier-Stokes equations in higher regularity with the aid of the initial-boundary and boundary layer weights using a recent Green’s function approach. The incompressible Euler limit follows as a byproduct of our framework.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"7 2","pages":""},"PeriodicalIF":2.8,"publicationDate":"2021-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40818-021-00108-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50517041","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: 20

Euler Equations on General Planar Domains 一般平面域上的欧拉方程

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-08-25 DOI: 10.1007/s40818-021-00107-0

Zonglin Han, Andrej Zlatoš

{"title":"Euler Equations on General Planar Domains","authors":"Zonglin Han, Andrej Zlatoš","doi":"10.1007/s40818-021-00107-0","DOIUrl":"10.1007/s40818-021-00107-0","url":null,"abstract":"<div><p>We obtain a general sufficient condition on the geometry of possibly singular planar domains that guarantees global uniqueness for any weak solution to the Euler equations on them whose vorticity is bounded and initially constant near the boundary. While similar existing results require domains that are <span>(C^{1,1})</span> except at finitely many convex corners, our condition involves much less domain smoothness, being only slightly more restrictive than the exclusion of corners with angles greater than <span>(pi )</span>. In particular, it is satisfied by all convex domains. The main ingredient in our approach is showing that constancy of the vorticity near the boundary is preserved for all time because Euler particle trajectories on these domains, even for general bounded solutions, cannot reach the boundary in finite time. We then use this to show that no vorticity can be created by the boundary of such possibly singular domains for general bounded solutions. We also show that our condition is essentially sharp in this sense by constructing domains that come arbitrarily close to satisfying it, and on which particle trajectories can reach the boundary in finite time. In addition, when the condition is satisfied, we find sharp bounds on the asymptotic rate of the fastest possible approach of particle trajectories to the boundary.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"7 2","pages":""},"PeriodicalIF":2.8,"publicationDate":"2021-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40818-021-00107-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50511555","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: 6

Global Well-Posedness for the Fifth-Order KdV Equation in (H^{-1}(pmb {mathbb {R}})) 五阶KdV方程在（H^｛-1｝（pmb｛mathbb｛R｝）中的全局适定性

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-08-25 DOI: 10.1007/s40818-021-00111-4

Bjoern Bringmann, Rowan Killip, Monica Visan

引用次数: 7

Maximal (L^q)-Regularity for Parabolic Hamilton–Jacobi Equations and Applications to Mean Field Games 抛物型Hamilton–Jacobi方程的极大正则性及其在平均场对策中的应用

IF 2.8 1区数学

Annals of Pde Pub Date : 2021-08-22 DOI: 10.1007/s40818-021-00109-y

Marco Cirant, Alessandro Goffi

引用次数: 20

Asymptotic Stability of Equilibria for Screened Vlasov–Poisson Systems via Pointwise Dispersive Estimates 基于点分散估计的屏蔽Vlasov–Poisson系统平衡的渐近稳定性