Annales De L Institut Henri Poincare-Analyse Non Lineaire最新文献_第5页

Collapsing and the convex hull property in a soap film capillarity model 肥皂膜毛细模型中的塌缩和凸壳性质

IF 1.9 1区数学

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-11-01 DOI: 10.1016/j.anihpc.2021.02.005

Darren King, Francesco Maggi, Salvatore Stuvard

引用次数: 8

Full cross-diffusion limit in the stationary Shigesada-Kawasaki-Teramoto model 平稳Shigesada-Kawasaki-Teramoto模型的完全交叉扩散极限

IF 1.9 1区数学

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-11-01 DOI: 10.1016/j.anihpc.2021.02.006

Kousuke Kuto

引用次数: 5

Vanishing viscosity limit of the 3D incompressible Oldroyd-B model 三维不可压缩Oldroyd-B模型的消失粘度极限

IF 1.9 1区数学

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-11-01 DOI: 10.1016/j.anihpc.2021.02.003

Ruizhao Zi

引用次数: 2

Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary 边界上具有常平均曲率的低维流形上的标量-平坦共形度量的紧性

IF 1.9 1区数学

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-11-01 DOI: 10.1016/j.anihpc.2021.01.005

Seunghyeok Kim , Monica Musso , Juncheng Wei

{"title":"Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary","authors":"Seunghyeok Kim , Monica Musso , Juncheng Wei","doi":"10.1016/j.anihpc.2021.01.005","DOIUrl":"10.1016/j.anihpc.2021.01.005","url":null,"abstract":"<div>We concern <math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math>-compactness of the solution set of the boundary Yamabe problem on smooth compact Riemannian manifolds with boundary provided that their dimensions are 4, 5 or 6. By conducting a quantitative analysis of a linear equation associated with the problem, we prove that the trace-free second fundamental form must vanish at possible blow-up points of a sequence of blowing-up solutions. Applying this result and the positive mass theorem, we deduce the <math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math>-compactness for all 4-manifolds (which may be non-umbilic). For the 5-dimensional case, we also establish that a sum of the second-order derivatives of the trace-free second fundamental form is non-negative at possible blow-up points. We essentially use this fact to obtain the <math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math>-compactness for all 5-manifolds. Finally, we show that the <math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math>-compactness on 6-manifolds is true if the trace-free second fundamental form on the boundary never vanishes.</div>","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.anihpc.2021.01.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72526945","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

Soliton resolution for the focusing modified KdV equation 聚焦修正KdV方程的孤子分辨率

IF 1.9 1区数学

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-11-01 DOI: 10.1016/j.anihpc.2021.02.008

Gong Chen , Jiaqi Liu

引用次数: 18

The influence of Einstein's effective viscosity on sedimentation at very small particle volume fraction 在非常小的颗粒体积分数下，爱因斯坦有效粘度对沉降的影响

IF 1.9 1区数学

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-11-01 DOI: 10.1016/j.anihpc.2021.02.001

Richard M. Höfer, Richard Schubert

{"title":"The influence of Einstein's effective viscosity on sedimentation at very small particle volume fraction","authors":"Richard M. Höfer, Richard Schubert","doi":"10.1016/j.anihpc.2021.02.001","DOIUrl":"10.1016/j.anihpc.2021.02.001","url":null,"abstract":"<div>We investigate the sedimentation of identical inertialess spherical particles in a Stokes fluid in the limit of many small particles. It is known that the presence of the particles leads to an increase of the effective viscosity of the suspension. By Einstein's formula this effect is of the order of the particle volume fraction ϕ. The disturbance of the fluid flow responsible for this increase of viscosity is very singular (like <math><msup><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></math>). Nevertheless, for well-prepared initial configurations and <math><mi>ϕ</mi><mo>→</mo><mn>0</mn></math>, we show that the microscopic dynamics is approximated to order <math><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>|</mo><mi>log</mi><mo>⁡</mo><mi>ϕ</mi><mo>|</mo></math> by a macroscopic coupled transport-Stokes system with an effective viscosity according to Einstein's formula. We provide quantitative estimates both for convergence of the densities in the p-Wasserstein distance for all p and for the fluid velocity in Lebesgue spaces in terms of the p-Wasserstein distance of the initial data. Our proof is based on approximations through the method of reflections and on a generalization of a classical result on convergence to mean-field limits in the infinite Wasserstein metric by Hauray.</div>","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.anihpc.2021.02.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82525811","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: 14

Non-existence of patterns and gradient estimates in semilinear elliptic equations with Neumann boundary conditions 具有Neumann边界条件的半线性椭圆方程模式的不存在性和梯度估计

IF 1.9 1区数学

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-11-01 DOI: 10.1016/j.anihpc.2021.02.002

Samuel Nordmann

{"title":"Non-existence of patterns and gradient estimates in semilinear elliptic equations with Neumann boundary conditions","authors":"Samuel Nordmann","doi":"10.1016/j.anihpc.2021.02.002","DOIUrl":"10.1016/j.anihpc.2021.02.002","url":null,"abstract":"<div>We call pattern any non-constant solution of a semilinear elliptic equation with Neumann boundary conditions. A classical theorem of Casten, Holland [20] and Matano [50] states that stable patterns do not exist in convex domains. In this article, we show that the assumptions of convexity of the domain and stability of the pattern in this theorem can be relaxed in several directions. In particular, we propose a general criterion for the non-existence of patterns, dealing with possibly non-convex domains and unstable patterns. Our results unfold the interplay between the geometry of the domain, the stability of patterns, and the <math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math> norm of the nonlinearity.In addition, we establish several gradient estimates for the patterns of (1). We prove a general nonlinear Cacciopoli inequality (or an inverse Poincaré inequality), stating that the <math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math>-norm of the gradient of a solution is controlled by the <math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math>-norm of <math><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo></math>, with a constant that only depends on the domain. This inequality holds for non-homogeneous equations. We also give several flatness estimates.Our approach relies on the introduction of what we call the Robin-curvature Laplacian. This operator is intrinsic to the domain and contains much information on how the geometry of the domain affects the shape of the solutions.Finally, we extend our results to unbounded domains. It allows us to improve the results of our previous paper [54] and to extend some results on De Giorgi's conjecture to a larger class of domains.</div>","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.anihpc.2021.02.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74196896","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: 3

Global regularity of 2D Navier–Stokes free boundary with small viscosity contrast 小粘度对比下二维Navier-Stokes自由边界的全局正则性

IF 1.9 1区数学

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2021-09-17 DOI: 10.4171/aihpc/74

F. Gancedo, Eduardo García-Juárez