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Mathematical analysis of the motion of a piston in a fluid with density dependent viscosity 活塞在粘性随密度变化的流体中运动的数学分析
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-09-07 DOI: 10.1007/s00028-024-01006-0
Vaibhav Kumar Jena, Debayan Maity, Abu Sufian
{"title":"Mathematical analysis of the motion of a piston in a fluid with density dependent viscosity","authors":"Vaibhav Kumar Jena, Debayan Maity, Abu Sufian","doi":"10.1007/s00028-024-01006-0","DOIUrl":"https://doi.org/10.1007/s00028-024-01006-0","url":null,"abstract":"<p>We study a free boundary value problem modelling the motion of a piston in a viscous compressible fluid. The fluid is modelled by 1D compressible Navier–Stokes equations with possibly degenerate viscosity coefficient, and the motion of the piston is described by Newton’s second law. We show that the initial boundary value problem has a unique global in time solution, and we also determine the large time behaviour of the system. Finally, we show how our methodology may be adapted to the motion of several pistons.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"46 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186949","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
Asymptotically almost periodic solutions for some partial differential inclusions in $$alpha $$ -norm $$alpha $$ -norm中某些偏微分夹杂的近似近周期解
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-09-07 DOI: 10.1007/s00028-024-01007-z
Mohamed Alia, Jaouad El Matloub, Khalil Ezzinbi
{"title":"Asymptotically almost periodic solutions for some partial differential inclusions in $$alpha $$ -norm","authors":"Mohamed Alia, Jaouad El Matloub, Khalil Ezzinbi","doi":"10.1007/s00028-024-01007-z","DOIUrl":"https://doi.org/10.1007/s00028-024-01007-z","url":null,"abstract":"<p>In this paper, we focus on investigating the existence of mild solutions and asymptotically almost periodic mild solutions for a class of partial differential inclusions. These inclusions involve a forcing multivalued function that relies on implicit spatial derivatives of the state variable. We introduce a novel approach to simplify the complexities associated with singularities when taking the <span>(alpha )</span>-norm.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"25 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186936","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
Periodic motions of species competition flows and inertial manifolds around them with nonautonomous diffusion 非自主扩散的物种竞争流及其周围惯性流形的周期运动
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-09-02 DOI: 10.1007/s00028-024-00997-0
Thi Ngoc Ha Vu, Thieu Huy Nguyen
{"title":"Periodic motions of species competition flows and inertial manifolds around them with nonautonomous diffusion","authors":"Thi Ngoc Ha Vu, Thieu Huy Nguyen","doi":"10.1007/s00028-024-00997-0","DOIUrl":"https://doi.org/10.1007/s00028-024-00997-0","url":null,"abstract":"<p>Motivated by the competition model of two species with nonautonomous diffusion, we consider fully nonautonomous parabolic evolution equation of the form <span>(frac{textrm{d}u}{textrm{d}t} + A(t)u(t) = f(t,u)+g(t))</span> in which the time-dependent family of linear partial differential operator <i>A</i>(<i>t</i>), the nonlinear term <i>f</i>(<i>t</i>, <i>u</i>), and the external force <i>g</i> is 1-periodic with respect to <i>t</i>. We prove the existence and uniqueness of a periodic solution of the above equation and study the inertial manifold for the solutions nearby that solution. We prove the existence of such an inertial manifold in the cases that the family of linear partial differential operators <span>((A(t))_{tin mathbb {R}})</span> generates an evolution family <span>((U(t,s))_{tge s})</span> satisfying certain dichotomy estimates, and the nonlinear term <i>f</i>(<i>t</i>, <i>x</i>) satisfies the <span>(varphi )</span>-Lipschitz condition, i.e., <span>(left| f(t,x_1)-f(t,x_2)right| leqslant varphi (t)left| A(t)^{theta } (x_1-x_2)right| )</span> where <span>(varphi (cdot ))</span> belongs to some admissible function space on the whole line. Then, we apply our abstract results to the above-mentioned competition model of two species with nonautonomous diffusion.\u0000</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"2022 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186951","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
Fine large-time asymptotics for the axisymmetric Navier–Stokes equations 轴对称纳维-斯托克斯方程的精细大时间渐近线
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-08-27 DOI: 10.1007/s00028-024-01001-5
Christian Seis, Dominik Winkler
{"title":"Fine large-time asymptotics for the axisymmetric Navier–Stokes equations","authors":"Christian Seis, Dominik Winkler","doi":"10.1007/s00028-024-01001-5","DOIUrl":"https://doi.org/10.1007/s00028-024-01001-5","url":null,"abstract":"<p>We examine the large-time behavior of axisymmetric solutions without swirl of the Navier–Stokes equation in <span>({mathbb {R}}^3)</span>. We construct higher-order asymptotic expansions for the corresponding vorticity. The appeal of this work lies in the simplicity of the applied techniques: Our approach is completely based on standard <span>(L^2)</span>-based entropy methods.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"5 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186952","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
Another remark on the global regularity issue of the Hall-magnetohydrodynamics system 关于霍尔磁流体动力学系统全局正则性问题的另一个评论
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-08-24 DOI: 10.1007/s00028-024-01000-6
Mohammad Mahabubur Rahman, Kazuo Yamazaki
{"title":"Another remark on the global regularity issue of the Hall-magnetohydrodynamics system","authors":"Mohammad Mahabubur Rahman, Kazuo Yamazaki","doi":"10.1007/s00028-024-01000-6","DOIUrl":"https://doi.org/10.1007/s00028-024-01000-6","url":null,"abstract":"<p>We discover new cancellations upon <span>(H^{2}(mathbb {R}^{n}))</span>-estimate of the Hall term, <span>(n in {2,3})</span>. Consequently, first, we derive a regularity criterion for the 3-dimensional Hall-magnetohydrodynamics system in terms of horizontal components of velocity and magnetic fields. Second, we are able to prove the global regularity of the <span>(2frac{1}{2})</span>-dimensional electron magnetohydrodynamics system with magnetic diffusion <span>((-Delta )^{frac{3}{2}} (b_{1}, b_{2}, 0) + (-Delta )^{alpha } (0, 0, b_{3}))</span> for <span>(alpha &gt; frac{1}{2})</span> despite the fact that <span>((-Delta )^{frac{3}{2}})</span> is the critical diffusive strength. Lastly, we extend this result to the <span>(2frac{1}{2})</span>-dimensional Hall-magnetohydrodynamics system with <span>(-Delta u)</span> replaced by <span>((-Delta )^{alpha } (u_{1}, u_{2}, 0) -Delta (0, 0, u_{3}))</span> for <span>(alpha &gt; frac{1}{2})</span>. The sum of the derivatives in diffusion that our result requires is <span>(11+ epsilon )</span> for any <span>(epsilon &gt; 0)</span>, while the sum for the classical <span>(2frac{1}{2})</span>-dimensional Hall-magnetohydrodynamics system is 12 considering <span>(-Delta u)</span> and <span>(-Delta b)</span>, of which its global regularity issue remains an outstanding open problem.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"43 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186953","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
Global strong solutions with large oscillations to the 3D full compressible Navier–Stokes equations without heat conductivity 无热传导的三维全可压缩纳维-斯托克斯方程具有大振荡的全局强解
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-08-24 DOI: 10.1007/s00028-024-01002-4
Haibo Yu
{"title":"Global strong solutions with large oscillations to the 3D full compressible Navier–Stokes equations without heat conductivity","authors":"Haibo Yu","doi":"10.1007/s00028-024-01002-4","DOIUrl":"https://doi.org/10.1007/s00028-024-01002-4","url":null,"abstract":"<p>We are concerned with the Cauchy problem to the three-dimensional full compressible Navier–Stokes equations with zero heat conductivity. Under the condition that the initial energy is small enough, global existence of strong solutions is established. Especially, the initial density is allowed to have large oscillations. The key to estimate the pointwise lower and upper bounds of the density lies in the handling of the energy conservation equation and the boundedness of the <span>(L^r)</span>–norm of the gradient of the pressure.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"46 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186954","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
A remark on selection of solutions for the transport equation 关于选择输运方程解的评论
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-08-22 DOI: 10.1007/s00028-024-00996-1
Jules Pitcho
{"title":"A remark on selection of solutions for the transport equation","authors":"Jules Pitcho","doi":"10.1007/s00028-024-00996-1","DOIUrl":"https://doi.org/10.1007/s00028-024-00996-1","url":null,"abstract":"<p>We prove that for bounded, divergence-free vector fields in <span>(L^1_textrm{loc}((0,+infty );BV_textrm{loc}(mathbb {R}^d;mathbb {R}^d)))</span>, regularisation by convolution of the vector field selects a single solution of the transport equation for any locally integrable initial datum. We recall the vector field constructed by Depauw in (C R Math Acad Sci Paris 337:249–252, 2003), which lies in the above class of vector fields. We show that the transport equation along this vector field has at least two bounded weak solutions for any bounded initial datum.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"8 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142186956","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
Damped Euler system with attractive Riesz interaction forces 具有吸引力里兹相互作用力的阻尼欧拉系统
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-08-08 DOI: 10.1007/s00028-024-00998-z
Young-Pil Choi, Jinwook Jung, Yoonjung Lee
{"title":"Damped Euler system with attractive Riesz interaction forces","authors":"Young-Pil Choi, Jinwook Jung, Yoonjung Lee","doi":"10.1007/s00028-024-00998-z","DOIUrl":"https://doi.org/10.1007/s00028-024-00998-z","url":null,"abstract":"<p>We consider the barotropic Euler equations with pairwise attractive Riesz interactions and linear velocity damping in the periodic domain. We establish the global-in-time well-posedness theory for the system near an equilibrium state if the coefficient of the Riesz interaction term is small. We also analyze the large-time behavior of solutions showing the exponential rate of convergence toward the equilibrium state as time goes to infinity.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"192 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930775","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
Global Cauchy problem for the Vlasov–Riesz–Fokker–Planck system near the global Maxwellian 全局麦克斯韦附近 Vlasov-Riesz-Fokker-Planck 系统的全局考奇问题
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-07-30 DOI: 10.1007/s00028-024-00995-2
Young-Pil Choi, In-Jee Jeong, Kyungkeun Kang
{"title":"Global Cauchy problem for the Vlasov–Riesz–Fokker–Planck system near the global Maxwellian","authors":"Young-Pil Choi, In-Jee Jeong, Kyungkeun Kang","doi":"10.1007/s00028-024-00995-2","DOIUrl":"https://doi.org/10.1007/s00028-024-00995-2","url":null,"abstract":"<p>We prove the global existence and uniqueness of solutions to the Vlasov–Riesz–Fokker–Planck system around the global Maxwellian in the periodic spatial domain. Depending on the order of Riesz potential, we present two frameworks for the construction of global-in-time solutions with Sobolev and analytic regularity. The analytic function framework covers the Vlasov–Dirac–Benney–Fokker–Planck system. Furthermore, we show the exponential decay of solutions toward the global Maxwellian. Our result is generalized to the whole space case in which the decay rate of convergence is algebraic.\u0000</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"124 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141863020","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
Spreading speeds and forced waves of a three species competition system with nonlocal dispersal in shifting habitats 变迁栖息地中具有非本地扩散性的三物种竞争系统的扩散速度和强迫波
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-07-28 DOI: 10.1007/s00028-024-00994-3
Jing Wang, Fei-Ying Yang, Wan-Tong Li
{"title":"Spreading speeds and forced waves of a three species competition system with nonlocal dispersal in shifting habitats","authors":"Jing Wang, Fei-Ying Yang, Wan-Tong Li","doi":"10.1007/s00028-024-00994-3","DOIUrl":"https://doi.org/10.1007/s00028-024-00994-3","url":null,"abstract":"<p>This paper is concerned with propagation phenomenon of a three species competition system with nonlocal dispersal in shifting habitats. We first give the existence of two types of forced wave connecting origin to only one species state and semi-co-existence state in supercritical and critical cases. Then, we get the existence of forced waves connecting origin to coexistence state at any speed. In particular, we establish the spreading property of the associated Cauchy problem depending on the range of the shifting speed which is identified respectively by (i) extinction of three species; (ii) only one species surviving; (iii) two species coexisting; (iv) persistence of three species.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"6 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776840","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
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