Journal de Mathematiques Pures et Appliquees最新文献_第9页

The existence of a weak solution for a compressible multicomponent fluid structure interaction problem 可压缩多组分流体结构相互作用问题的弱解存在性

IF 2.3 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-03-04 DOI: 10.1016/j.matpur.2024.02.007

Martin Kalousek , Sourav Mitra , Šárka Nečasová

{"title":"The existence of a weak solution for a compressible multicomponent fluid structure interaction problem","authors":"Martin Kalousek , Sourav Mitra , Šárka Nečasová","doi":"10.1016/j.matpur.2024.02.007","DOIUrl":"10.1016/j.matpur.2024.02.007","url":null,"abstract":"<div>We analyze a system of PDEs governing the interaction between two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time dependent 3D domain filled by the fluids. The dynamics of the fluids is modeled by a system resembling compressible Navier-Stokes equations with a physically realistic pressure depending on densities of both the fluids. The shell possesses a non-linear, non-convex Koiter energy. Considering that the densities are comparable initially we prove the existence of a weak solution until the degeneracy of the energy or the self-intersection of the structure occurs for two cases. In the first case the adiabatic exponents are assumed to satisfy <math><mi>max</mi><mo>⁡</mo><mo>{</mo><mi>γ</mi><mo>,</mo><mi>β</mi><mo>}</mo><mo>></mo><mn>2</mn></math>, <math><mi>min</mi><mo>⁡</mo><mo>{</mo><mi>γ</mi><mo>,</mo><mi>β</mi><mo>}</mo><mo>></mo><mn>0</mn></math>, and the structure involved is assumed to be non-dissipative. For the second case we assume the critical case <math><mi>max</mi><mo>⁡</mo><mo>{</mo><mi>γ</mi><mo>,</mo><mi>β</mi><mo>}</mo><mo>≥</mo><mn>2</mn></math> and <math><mi>min</mi><mo>⁡</mo><mo>{</mo><mi>γ</mi><mo>,</mo><mi>β</mi><mo>}</mo><mo>></mo><mn>0</mn></math> and the dissipativity of the structure. The result is achieved in several steps involving, extension of the physical domain, penalization of the interface condition, artificial regularization of the shell energy and the pressure, the almost compactness argument, added structural dissipation and suitable limit passages depending on uniform estimates.</div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"184 ","pages":"Pages 118-189"},"PeriodicalIF":2.3,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140047475","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

Higher order interpolative geometries and gradient regularity in evolutionary obstacle problems 进化障碍问题中的高阶内插几何和梯度正则性

IF 2.3 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-03-04 DOI: 10.1016/j.matpur.2024.02.006

Sunghan Kim, Kaj Nyström

{"title":"Higher order interpolative geometries and gradient regularity in evolutionary obstacle problems","authors":"Sunghan Kim, Kaj Nyström","doi":"10.1016/j.matpur.2024.02.006","DOIUrl":"10.1016/j.matpur.2024.02.006","url":null,"abstract":"<div>We prove new optimal <math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>α</mi></mrow></msup></math> regularity results for obstacle problems involving evolutionary p-Laplace type operators in the degenerate regime <math><mi>p</mi><mo>></mo><mn>2</mn></math>. Our main results include the optimal regularity improvement at free boundary points in intrinsic backward p-paraboloids, up to the critical exponent, <math><mi>α</mi><mo>≤</mo><mn>2</mn><mo>/</mo><mo>(</mo><mi>p</mi><mo>−</mo><mn>2</mn><mo>)</mo></math>, and the optimal regularity across the free boundaries in the full cylinders up to a universal threshold. Moreover, we provide an intrinsic criterion by which the optimal regularity improvement at free boundaries can be extended to the entire cylinders. An important feature of our analysis is that we do not impose any assumption on the time derivative of the obstacle. Our results are formulated in function spaces associated to what we refer to as higher order or <math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>α</mi></mrow></msup></math> intrinsic interpolative geometries.</div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"185 ","pages":"Pages 1-46"},"PeriodicalIF":2.3,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021782424000266/pdfft?md5=3fbde8e03d141f6fd4be7e7aa45c36ea&pid=1-s2.0-S0021782424000266-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140047406","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

On nonlinear instability of Prandtl's boundary layers: The case of Rayleigh's stable shear flows 论普朗特边界层的非线性不稳定性：瑞利稳定剪切流的情况

IF 2.3 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-03-02 DOI: 10.1016/j.matpur.2024.02.001

Emmanuel Grenier , Toan T. Nguyen

{"title":"On nonlinear instability of Prandtl's boundary layers: The case of Rayleigh's stable shear flows","authors":"Emmanuel Grenier , Toan T. Nguyen","doi":"10.1016/j.matpur.2024.02.001","DOIUrl":"10.1016/j.matpur.2024.02.001","url":null,"abstract":"<div>In 1904, Prandtl introduced his famous boundary layer in order to describe the behavior of solutions of Navier Stokes equations near a boundary as the viscosity goes to 0. His Ansatz has later been justified for analytic data by R.E. Caflisch and M. Sammartino. In this paper, we prove that his expansion is false, up to <math><mi>O</mi><mo>(</mo><msup><mrow><mi>ν</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></msup><mo>)</mo></math> order terms in <math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math> norm, in the case of solutions with Sobolev regularity, even in cases where the Prandlt's equation is well posed in Sobolev spaces.In addition, we also prove that monotonic boundary layer profiles, which are stable when <math><mi>ν</mi><mo>=</mo><mn>0</mn></math>, are nonlinearly unstable when <math><mi>ν</mi><mo>></mo><mn>0</mn></math>, provided ν is small enough, up to <math><mi>O</mi><mo>(</mo><msup><mrow><mi>ν</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></msup><mo>)</mo></math> terms in <math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math> norm.</div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"184 ","pages":"Pages 71-90"},"PeriodicalIF":2.3,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140047730","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

Migrating elastic flows 迁移弹性流量

IF 2.3 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-03-01 DOI: 10.1016/j.matpur.2024.02.003

Tomoya Kemmochi , Tatsuya Miura

引用次数: 0

Minimal solutions of master equations for extended mean field games 扩展均值场博弈主方程的最小解

IF 2.3 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-03-01 DOI: 10.1016/j.matpur.2024.02.002

Chenchen Mou , Jianfeng Zhang

{"title":"Minimal solutions of master equations for extended mean field games","authors":"Chenchen Mou , Jianfeng Zhang","doi":"10.1016/j.matpur.2024.02.002","DOIUrl":"10.1016/j.matpur.2024.02.002","url":null,"abstract":"<div>In an extended mean field game the vector field governing the flow of the population can be different from that of the individual player at some mean field equilibrium. This new class strictly includes the standard mean field games. It is well known that, without any monotonicity conditions, mean field games typically contain multiple mean field equilibria and the wellposedness of their corresponding master equations fails. In this paper, a partial order for the set of probability measure flows is proposed to compare different mean field equilibria. The minimal and maximal mean field equilibria under this partial order are constructed and satisfy the flow property. The corresponding value functions, however, are in general discontinuous. We thus introduce a notion of weak-viscosity solutions for the master equation and verify that the value functions are indeed weak-viscosity solutions. Moreover, a comparison principle for weak-viscosity semi-solutions is established and thus these two value functions serve as the minimal and maximal weak-viscosity solutions in appropriate sense. In particular, when these two value functions coincide, the value function becomes the unique weak-viscosity solution to the master equation. The novelties of the work persist even when restricted to the standard mean field games.</div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"184 ","pages":"Pages 190-217"},"PeriodicalIF":2.3,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140047916","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

Fast fusion in a two-dimensional coagulation model 二维凝固模型中的快速融合

IF 2.3 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-03-01 DOI: 10.1016/j.matpur.2024.02.004

Iulia Cristian , Juan J.L. Velázquez

引用次数: 0

A geometrisation of N-manifolds N 个网格的几何解析

IF 2.3 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-03-01 DOI: 10.1016/j.matpur.2024.02.005

M. Heuer, M. Jotz

引用次数: 0

A global branch approach to normalized solutions for the Schrödinger equation 薛定谔方程归一化解的全局分支方法

IF 2.3 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-02-01 DOI: 10.1016/j.matpur.2024.01.004

Louis Jeanjean , Jianjun Zhang , Xuexiu Zhong

引用次数: 0

The primitive equations with stochastic wind driven boundary conditions 带有随机风驱动边界条件的原始方程

IF 2.3 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-02-01 DOI: 10.1016/j.matpur.2024.01.001

Tim Binz , Matthias Hieber , Amru Hussein , Martin Saal

引用次数: 0

Stability of the separable solutions for a nonlinear boundary diffusion problem 非线性边界扩散问题可分离解的稳定性

IF 2.3 1区数学

Journal de Mathematiques Pures et Appliquees Pub Date : 2024-02-01 DOI: 10.1016/j.matpur.2024.01.002

Tianling Jin , Jingang Xiong , Xuzhou Yang

引用次数: 0