Journal of Dynamics and Differential Equations最新文献

{"title":"On the Failure of Linearization for Germs of $$C^1$$ Hyperbolic Vector Fields in Dimension One","authors":"Hélène Eynard-Bontemps, Andrés Navas","doi":"10.1007/s10884-023-10330-x","DOIUrl":"https://doi.org/10.1007/s10884-023-10330-x","url":null,"abstract":"<p>We investigate conjugacy classes of germs of hyperbolic 1-dimensional vector fields at the origin in low regularity. We show that the classical linearization theorem of Sternberg strongly fails in this setting by providing explicit uncountable families of mutually non-conjugate flows with the same multipliers, where conjugacy is considered in the bi-Lipschitz, <span>(C^1)</span> and <span>(C^{1+ac})</span> settings.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"173 3 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138547649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Center Stable Manifolds Around Line Solitary Waves of the Zakharov–Kuznetsov Equation","authors":"Yohei Yamazaki","doi":"10.1007/s10884-023-10329-4","DOIUrl":"https://doi.org/10.1007/s10884-023-10329-4","url":null,"abstract":"<p>In this paper, we construct center stable manifolds of unstable line solitary waves for the Zakharov–Kuznetsov equation on <span>({mathbb {R}} times {mathbb {T}}_L)</span> and show the orbital stability of the unstable line solitary waves on the center stable manifolds, which yields the asymptotic stability of unstable solitary waves on the center stable manifolds near by stable line solitary waves. The construction is based on the graph transform approach by Nakanishi and Schlag (SIAM J Math Anal 44:1175–1210, 2012). Applying the bilinear estimate on Fourier restriction spaces by Molinet and Pilod (Ann Inst H Poincaré Anal Non Lineaire 32:347–371, 2015) and modifying the mobile distance in Nakanishi and Schlag (2012), we construct a contraction map on the graph space.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"66 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138524967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Well-Posedness and Singularity Formation for the Kolmogorov Two-Equation Model of Turbulence in 1-D","authors":"Francesco Fanelli, Rafael Granero-Belinchón","doi":"10.1007/s10884-023-10326-7","DOIUrl":"https://doi.org/10.1007/s10884-023-10326-7","url":null,"abstract":"We study the Kolomogorov two-equation model of turbulence in one space dimension. Two are the main results of the paper. First of all, we establish a local well-posedness theory in Sobolev spaces even in the case of vanishing mean turbulent kinetic energy. Then, we show that there are smooth solutions which blow up in finite time. To the best of our knowledge, these results are the first establishing the well-posedness of the system for vanishing initial data and the occurence of finite time singularities for the model under study.","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"23 49","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135545535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of Interacting Monomial Scalar Field Potentials and Perfect Fluids","authors":"Artur Alho, Vitor Bessa, Filipe C. Mena","doi":"10.1007/s10884-023-10318-7","DOIUrl":"https://doi.org/10.1007/s10884-023-10318-7","url":null,"abstract":"Abstract Motivated by cosmological models of the early universe we analyse the dynamics of the Einstein equations with a minimally coupled scalar field with monomial potentials $$V(phi )=frac{(lambda phi )^{2n}}{2n}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;V&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;ϕ&lt;/mml:mi&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:mfrac&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;λ&lt;/mml:mi&gt; &lt;mml:mi&gt;ϕ&lt;/mml:mi&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:mfrac&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; , $$lambda &gt;0$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;λ&lt;/mml:mi&gt; &lt;mml:mo&gt;&gt;&lt;/mml:mo&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; , $$nin {mathbb {N}}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;mml:mo&gt;∈&lt;/mml:mo&gt; &lt;mml:mi&gt;N&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; , interacting with a perfect fluid with linear equation of state $$p_{textrm{pf}}=(gamma _{textrm{pf}}-1)rho _{textrm{pf}}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;p&lt;/mml:mi&gt; &lt;mml:mtext&gt;pf&lt;/mml:mtext&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;γ&lt;/mml:mi&gt; &lt;mml:mtext&gt;pf&lt;/mml:mtext&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;-&lt;/mml:mo&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;ρ&lt;/mml:mi&gt; &lt;mml:mtext&gt;pf&lt;/mml:mtext&gt; &lt;/mml:msub&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; , $$gamma _{textrm{pf}}in (0,2)$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;γ&lt;/mml:mi&gt; &lt;mml:mtext&gt;pf&lt;/mml:mtext&gt; &lt;/mml:msub&gt; &lt;mml:mo&gt;∈&lt;/mml:mo&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; , in flat Robertson–Walker spacetimes. The interaction is a friction-like term of the form $$Gamma (phi )=mu phi ^{2p}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;Γ&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mo&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;ϕ&lt;/mml:mi&gt; &lt;mml:mo&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:mi&gt;μ&lt;/mml:mi&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;ϕ&lt;/mml:mi&gt; &lt;mml:mrow&gt; &lt;mml:mn&gt;2&lt;/mml:mn&gt; &lt;mml:mi&gt;p&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;/mml:msup&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; , $$mu &gt;0$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;μ&lt;/mml:mi&gt; &lt;mml:mo&gt;&gt;&lt;/mml:mo&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; , $$pin {mathbb {N}}cup {0}$$ &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;p&lt;/mml:mi&gt; &lt;mml:mo&gt;∈&lt;/mml:mo&gt; &lt;mml:mi&gt;N&lt;/mml:mi&gt; &lt;mml:mo&gt;∪&lt;/mml:mo&gt; &lt;mml:mo&gt;{&lt;/mml:mo&gt; &lt;mml:mn&gt;0&lt;/mml:mn&gt; &lt;mml:mo&gt;}&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;/mml:math&gt; . The analysis relies on the introduction of a new regular 3-dimensional dynamical systems’ formulation of the Einstein equations on a compact state space, and the use of dynamical systems’ tools such as qua","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135634809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On weak/Strong Attractor for a 3-D Structural-Acoustic Interaction with Kirchhoff–Boussinesq Elastic Wall Subject to Restricted Boundary Dissipation","authors":"Irena Lasiecka, José H. Rodrigues","doi":"10.1007/s10884-023-10325-8","DOIUrl":"https://doi.org/10.1007/s10884-023-10325-8","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136159439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Boundedness and Stabilization in a Stage-Structured Predator–Prey Model with Two Taxis Mechanisms","authors":"Changfeng Liu, Shangjiang Guo","doi":"10.1007/s10884-023-10324-9","DOIUrl":"https://doi.org/10.1007/s10884-023-10324-9","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"20 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136234518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Topological Entropy of Saturated Sets for Amenable Group Actions","authors":"Xiankun Ren, Xueting Tian, Yunhua Zhou","doi":"10.1007/s10884-023-10302-1","DOIUrl":"https://doi.org/10.1007/s10884-023-10302-1","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136262829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Optimal Halanay Inequality and Decay Rate of Solutions to Some Classes of Nonlocal Functional Differential Equations","authors":"Tran Dinh Ke, Nguyen Nhu Thang","doi":"10.1007/s10884-023-10323-w","DOIUrl":"https://doi.org/10.1007/s10884-023-10323-w","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"48 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135513170","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonautonomous Normal Forms with Parameters","authors":"Luís Barreira, Claudia Valls","doi":"10.1007/s10884-023-10315-w","DOIUrl":"https://doi.org/10.1007/s10884-023-10315-w","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135617779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Note on the Polynomially Attracting Sets for Dynamical Systems","authors":"Xiangming Zhu, Chengkui Zhong","doi":"10.1007/s10884-023-10322-x","DOIUrl":"https://doi.org/10.1007/s10884-023-10322-x","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"9 32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135567054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}