Mathematische Nachrichten最新文献

{"title":"The energy decay rate of a transmission system governed by the degenerate wave equation with drift and under heat conduction with the memory effect","authors":"Mohammad Akil,&nbsp;Genni Fragnelli,&nbsp;Ibtissam Issa","doi":"10.1002/mana.202300571","DOIUrl":"10.1002/mana.202300571","url":null,"abstract":"<p>In this paper, we investigate the stabilization of the transmission problem of the degenerate wave equation and the heat equation under the Coleman–Gurtin heat conduction law or Gurtin–Pipkin law with the memory effect. We investigate the polynomial stability of this system when employing the Coleman–Gurtin heat conduction, establishing a decay rate of type <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>t</mi>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$t^{-4}$</annotation>\u0000 </semantics></math>. Next, we demonstrate exponential stability in the case when Gurtin–Pipkin heat conduction is applied.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871436","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}

{"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,&nbsp;Vladimir Georgiev","doi":"10.1002/mana.202300253","DOIUrl":"10.1002/mana.202300253","url":null,"abstract":"<p>The work deals with the Ericksen–Leslie system for nematic liquid crystals on the space <span></span><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 <span></span><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 <span></span><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 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"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}

{"title":"On the Cauchy problem for a two-component higher order Camassa–Holm system","authors":"Shouming Zhou,&nbsp;Luhang Zhou,&nbsp;Rong Chen","doi":"10.1002/mana.202300382","DOIUrl":"10.1002/mana.202300382","url":null,"abstract":"&lt;p&gt;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 &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$B_{p,1}^{frac{1}{p}} times B_{p,1}^{2+frac{1}{p}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$1 le p &amp;lt; infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, 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 &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$B_{p,infty }^{s","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"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}

{"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":"&lt;p&gt;In the framework of quasi-regular strongly local Dirichlet form &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(mathcal {E},D(mathcal {E}))$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$L^2(X;mathfrak {m})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; admitting minimal &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {E}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-dominant measure &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;annotation&gt;$mu$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, we construct a natural &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-energy functional &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;E&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(mathcal {E}^{,p},D(mathcal {E}^{,p}))$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$L^p(X;mathfrak {m})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"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}

{"title":"Boundedness in a quasilinear forager–exploiter model","authors":"Jianping Wang,&nbsp;Qianying Zhang","doi":"10.1002/mana.202300507","DOIUrl":"10.1002/mana.202300507","url":null,"abstract":"<p>We study a forager–exploiter model with nonlinear diffusions:\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871437","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}

{"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,&nbsp;Pablo Galindo,&nbsp;Andriy Zagorodnyuk","doi":"10.1002/mana.202300415","DOIUrl":"10.1002/mana.202300415","url":null,"abstract":"<p>We obtain a complete description of the spectrum of the Fréchet algebra of symmetric analytic functions bounded on balls on the sequence space <span></span><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 <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>ℓ</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$ell _p$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>≤</mo>\u0000 <mi>p</mi>\u0000 <mo>&lt;</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$1le p &amp;lt;infty$</annotation>\u0000 </semantics></math>, the radius function of any evaluation homomorphism <span></span><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 <span></span><math>\u0000 <semantics>\u0000 <mi>x</mi>\u0000 <annotation>$x$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"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}

{"title":"Weighted Kato–Ponce inequalities for multiple factors","authors":"Sean Douglas,&nbsp;Loukas Grafakos","doi":"10.1002/mana.202300443","DOIUrl":"10.1002/mana.202300443","url":null,"abstract":"<p>In this paper, we establish a weighted Kato–Ponce inequality for <span></span><math>\u0000 <semantics>\u0000 <mi>m</mi>\u0000 <annotation>$m$</annotation>\u0000 </semantics></math> factors in the endpoint case. Furthermore, we extend the validity of the Kato–Ponce inequality from the class of Schwartz functions to the broader class of functions living in a (weighted) fractional Sobolev space.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780450","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}

{"title":"On differentiability of Sobolev functions with respect to the Sobolev norm","authors":"Vladimir Gol'dshtein,&nbsp;Paz Hashash,&nbsp;Alexander Ukhlov","doi":"10.1002/mana.202300545","DOIUrl":"10.1002/mana.202300545","url":null,"abstract":"<p>We study connections between the <span></span><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 <span></span><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 <span></span><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 <span></span><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 <span></span><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 <span></span><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.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"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}

{"title":"Wong–Zakai approximation for a stochastic 2D Cahn–Hilliard–Navier–Stokes model","authors":"T. Tachim Medjo","doi":"10.1002/mana.202400065","DOIUrl":"10.1002/mana.202400065","url":null,"abstract":"<p>In this paper, we demonstrate the Wong–Zakai approximation results for two dimensional stochastic Cahn–Hilliard–Navier–Stokes model. The model consists of a Navier–Stokes system coupled with convective Cahn–Hilliard equations. It describes the motion of an incompressible isothermal mixture of two (partially) immiscible fluids under the influence of multiplicative noise. Our main result describes the support of the distribution of solutions. As in [2], both inclusions are proved by means of a general Wong–Zakai type result of convergence in probability for nonlinear stochastic PDEs driven by a Hilbert-valued Brownian motion and some adapted finite-dimensional approximation of this process. Note that the coupling between the Navier–Stokes system and the Cahn–Hilliard equations makes the analysis more involved.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141738411","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}

{"title":"Fractional operators with homogeneous kernel on the Calderón product of Morrey spaces","authors":"Daniel Salim,&nbsp;Moch. Taufik Hakiki,&nbsp;Yoshihiro Sawano,&nbsp;Denny Ivanal Hakim,&nbsp;Muhamad Jamaludin","doi":"10.1002/mana.202400043","DOIUrl":"10.1002/mana.202400043","url":null,"abstract":"<p>We investigate fractional operators with homogeneous kernel in Morrey spaces. In particular, we prove that fractional integral operators and fractional maximal operators with homogeneous kernel are bounded from the Calderón product of Morrey spaces to certain Morrey spaces. Our results can be seen as a generalization of a recent result on the relation between the boundedness of (classical) fractional operators and interpolation of Morrey spaces. What is new about this paper is not only the passage from the classical fractional integral operators to the rough integral operators. Even the case of fractional integral operators, handled in earlier papers, is significantly simplified.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141649264","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}