Mathematische Nachrichten最新文献_第10页

Local and global solutions on arcs for the Ericksen–Leslie problem in R N $mathbb {R}^N$ RN$mathbb {R}^N$ 中埃里克森-莱斯利问题弧上的局部和全局解

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-07-29 DOI: 10.1002/mana.202300253

Daniele Barbera, Vladimir Georgiev

{"title":"Local and global solutions on arcs for the Ericksen–Leslie problem in \u0000 \u0000 \u0000 R\u0000 N\u0000 \u0000 $mathbb {R}^N$","authors":"Daniele Barbera, Vladimir Georgiev","doi":"10.1002/mana.202300253","DOIUrl":"10.1002/mana.202300253","url":null,"abstract":"The work deals with the Ericksen–Leslie system for nematic liquid crystals on the space <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>N</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^N$</annotation>\u0000 </semantics></math> with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>≥</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$Nge 3$</annotation>\u0000 </semantics></math>. In our work, we suppose the initial condition <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>v</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$v_0$</annotation>\u0000 </semantics></math> stays on an arc connecting two fixed orthogonal vectors on the unit sphere. Thanks to this geometric assumption, we prove through energy a priori estimates the local existence and the global existence for small initial data of a solution\u0000\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 10","pages":"3584-3624"},"PeriodicalIF":0.8,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

On the Cauchy problem for a two-component higher order Camassa–Holm system 关于双分量高阶卡马萨-霍姆系统的考奇问题

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-07-29 DOI: 10.1002/mana.202300382

Shouming Zhou, Luhang Zhou, Rong Chen

{"title":"On the Cauchy problem for a two-component higher order Camassa–Holm system","authors":"Shouming Zhou, Luhang Zhou, Rong Chen","doi":"10.1002/mana.202300382","DOIUrl":"10.1002/mana.202300382","url":null,"abstract":"In this paper, we focus on the well-posedness, blow-up phenomena, and continuity of the data-to-solution map of the Cauchy problem for a two-component higher order Camassa–Holm (CH) system. The local well-posedness is established in Besov spaces <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>B</mi>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mfrac>\u0000 <mn>1</mn>\u0000 <mi>p</mi>\u0000 </mfrac>\u0000 </msubsup>\u0000 <mo>×</mo>\u0000 <msubsup>\u0000 <mi>B</mi>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mo>+</mo>\u0000 <mfrac>\u0000 <mn>1</mn>\u0000 <mi>p</mi>\u0000 </mfrac>\u0000 </mrow>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation>$B_{p,1}^{frac{1}{p}} times B_{p,1}^{2+frac{1}{p}}$</annotation>\u0000 </semantics></math> with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>≤</mo>\u0000 <mi>p</mi>\u0000 <mo><</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$1 le p &lt; infty$</annotation>\u0000 </semantics></math>, which improves the local well-posedness result proved before in Tang and Liu [Z. Angew. Math. Phys. 66 (2015), 1559–1580], Ye and Yin [arXiv preprint arXiv:2109.00948 (2021)], Zhang and Li [Nonlinear Anal. Real World Appl. 35 (2017), 414–440], and Zhou [Math. Nachr. 291 (2018), no. 10, 1595–1619]. Next, we consider the continuity of the solution-to-data map, that is, the ill-posedness is derived in Besov space <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>B</mi>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msubsup>\u0000 <mo>×</mo>\u0000 <msubsup>\u0000 <mi>B</mi>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <mi>s</mi>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation>$B_{p,infty }^{s","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 10","pages":"3797-3834"},"PeriodicalIF":0.8,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

( 1 , p ) $(1,p)$ -Sobolev spaces based on strongly local Dirichlet forms 基于强局部 Dirichlet 形式的 (1,p)$(1,p)$-Sobolev 空间

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-07-29 DOI: 10.1002/mana.202400025

Kazuhiro Kuwae

{"title":"(\u0000 1\u0000 ,\u0000 p\u0000 )\u0000 \u0000 $(1,p)$\u0000 -Sobolev spaces based on strongly local Dirichlet forms","authors":"Kazuhiro Kuwae","doi":"10.1002/mana.202400025","DOIUrl":"10.1002/mana.202400025","url":null,"abstract":"In the framework of quasi-regular strongly local Dirichlet form <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>E</mi>\u0000 <mo>,</mo>\u0000 <mi>D</mi>\u0000 <mo>(</mo>\u0000 <mi>E</mi>\u0000 <mo>)</mo>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(mathcal {E},D(mathcal {E}))$</annotation>\u0000 </semantics></math> on <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>;</mo>\u0000 <mi>m</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$L^2(X;mathfrak {m})$</annotation>\u0000 </semantics></math> admitting minimal <math>\u0000 <semantics>\u0000 <mi>E</mi>\u0000 <annotation>$mathcal {E}$</annotation>\u0000 </semantics></math>-dominant measure <math>\u0000 <semantics>\u0000 <mi>μ</mi>\u0000 <annotation>$mu$</annotation>\u0000 </semantics></math>, we construct a natural <math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-energy functional <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>E</mi>\u0000 <mrow>\u0000 <mspace></mspace>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <mi>D</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>E</mi>\u0000 <mrow>\u0000 <mspace></mspace>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(mathcal {E}^{,p},D(mathcal {E}^{,p}))$</annotation>\u0000 </semantics></math> on <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>X</mi>\u0000 <mo>;</mo>\u0000 <mi>m</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$L^p(X;mathfrak {m})$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 10","pages":"3723-3740"},"PeriodicalIF":0.8,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Boundedness in a quasilinear forager–exploiter model 准线性觅食者--开发者模型中的有界性

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-07-29 DOI: 10.1002/mana.202300507

Jianping Wang, Qianying Zhang

引用次数: 0

On the spectrum of the algebra of bounded-type symmetric analytic functions on ℓ 1 $ell _1$ 论 ℓ1$ell _1$ 上有界型对称解析函数代数的谱

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-07-29 DOI: 10.1002/mana.202300415

Iryna Chernega, Pablo Galindo, Andriy Zagorodnyuk

{"title":"On the spectrum of the algebra of bounded-type symmetric analytic functions on \u0000 \u0000 \u0000 ℓ\u0000 1\u0000 \u0000 $ell _1$","authors":"Iryna Chernega, Pablo Galindo, Andriy Zagorodnyuk","doi":"10.1002/mana.202300415","DOIUrl":"10.1002/mana.202300415","url":null,"abstract":"We obtain a complete description of the spectrum of the Fréchet algebra of symmetric analytic functions bounded on balls on the sequence space <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ℓ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$ell _1$</annotation>\u0000 </semantics></math>. This is achieved after proving that on the analogous algebra for <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ℓ</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$ell _p$</annotation>\u0000 </semantics></math>, <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>≤</mo>\u0000 <mi>p</mi>\u0000 <mo><</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$1le p &lt;infty$</annotation>\u0000 </semantics></math>, the radius function of any evaluation homomorphism <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>δ</mi>\u0000 <mi>x</mi>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mi>x</mi>\u0000 <mo>∈</mo>\u0000 <msub>\u0000 <mi>ℓ</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$delta _x, nobreakspace x in ell _p$</annotation>\u0000 </semantics></math>, coincides with the norm of <math>\u0000 <semantics>\u0000 <mi>x</mi>\u0000 <annotation>$x$</annotation>\u0000 </semantics></math>.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 10","pages":"3835-3846"},"PeriodicalIF":0.8,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Weighted Kato–Ponce inequalities for multiple factors 多因素加权卡托-庞斯不等式

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-07-22 DOI: 10.1002/mana.202300443

Sean Douglas, Loukas Grafakos

引用次数: 0

On differentiability of Sobolev functions with respect to the Sobolev norm 关于索波列函数与索波列规范的可微分性

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-07-22 DOI: 10.1002/mana.202300545

Vladimir Gol'dshtein, Paz Hashash, Alexander Ukhlov

{"title":"On differentiability of Sobolev functions with respect to the Sobolev norm","authors":"Vladimir Gol'dshtein, Paz Hashash, Alexander Ukhlov","doi":"10.1002/mana.202300545","DOIUrl":"10.1002/mana.202300545","url":null,"abstract":"We study connections between the <math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>W</mi>\u0000 <mi>p</mi>\u0000 <mn>1</mn>\u0000 </msubsup>\u0000 <annotation>$W^1_p$</annotation>\u0000 </semantics></math>-differentiability and the <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$L_p$</annotation>\u0000 </semantics></math>-differentiability of Sobolev functions. We prove that <math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>W</mi>\u0000 <mi>p</mi>\u0000 <mn>1</mn>\u0000 </msubsup>\u0000 <annotation>$W^1_p$</annotation>\u0000 </semantics></math>-differentiability implies the <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$L_p$</annotation>\u0000 </semantics></math>-differentiability, but the opposite implication is not valid. The notion of approximate differentiability is discussed as well. In addition, we consider the <math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>W</mi>\u0000 <mi>p</mi>\u0000 <mn>1</mn>\u0000 </msubsup>\u0000 <annotation>$W^1_p$</annotation>\u0000 </semantics></math>-differentiability of Sobolev functions <math>\u0000 <semantics>\u0000 <msub>\u0000 <mo>cap</mo>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$operatorname{cap}_p$</annotation>\u0000 </semantics></math>-almost everywhere.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 10","pages":"3681-3699"},"PeriodicalIF":0.8,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300545","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Wong–Zakai approximation for a stochastic 2D Cahn–Hilliard–Navier–Stokes model 随机二维 Cahn-Hilliard-Navier-Stokes 模型的 Wong-Zakai 近似值

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-07-19 DOI: 10.1002/mana.202400065

T. Tachim Medjo

引用次数: 0

Fractional operators with homogeneous kernel on the Calderón product of Morrey spaces 莫雷空间卡尔德龙积上具有同质核的分数算子

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-07-15 DOI: 10.1002/mana.202400043

Daniel Salim, Moch. Taufik Hakiki, Yoshihiro Sawano, Denny Ivanal Hakim, Muhamad Jamaludin

引用次数: 0

L 2 $L^{2}$ -growth property for the wave equation with a higher derivative term 带有高导数项的波方程的 L2$L^{2}$ 生长特性

IF 0.8 3区数学

Mathematische Nachrichten Pub Date : 2024-07-15 DOI: 10.1002/mana.202300358

Xiaoyan Li, Ryo Ikehata

{"title":"L\u0000 2\u0000 \u0000 $L^{2}$\u0000 -growth property for the wave equation with a higher derivative term","authors":"Xiaoyan Li, Ryo Ikehata","doi":"10.1002/mana.202300358","DOIUrl":"10.1002/mana.202300358","url":null,"abstract":"We consider the Cauchy problem in <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>${bf R}^{n}$</annotation>\u0000 </semantics></math> for the wave equation with a higher derivative term. We derive sharp growth estimates of the <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^{2}$</annotation>\u0000 </semantics></math>-norm of the solution itself for the case of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$n = 1$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$n = 2$</annotation>\u0000 </semantics></math>. By imposing the weighted <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$L^{1}$</annotation>\u0000 </semantics></math>-initial velocity, we can get the lower and upper bound estimates of the solution itself. For the case of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>≥</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$nge 3$</annotation>\u0000 </semantics></math>, we observe that the <math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^{2}$</annotation>\u0000 </semantics></math>-growth behavior of the solution never occurs in the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>∩</mo>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(L^{2}cap L^{1})$</annotation>\u0000 </semantics></math>-framework of the initial data.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 10","pages":"3625-3640"},"PeriodicalIF":0.8,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141648443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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