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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
Stability of random attractors for non-autonomous fractional stochastic p-Laplacian equations driven by nonlinear colored noise 非线性彩色噪声驱动的非自治分数随机 p-Laplacian 方程随机吸引子的稳定性
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-07-23 DOI: 10.1007/s00028-024-00993-4
Xuping Zhang, Ru Tian, Donal O’Regan
{"title":"Stability of random attractors for non-autonomous fractional stochastic p-Laplacian equations driven by nonlinear colored noise","authors":"Xuping Zhang, Ru Tian, Donal O’Regan","doi":"10.1007/s00028-024-00993-4","DOIUrl":"https://doi.org/10.1007/s00028-024-00993-4","url":null,"abstract":"<p>The aim of this paper is to establish the stability of pullback random attractors of non-autonomous fractional stochastic <i>p</i>-Laplacian equations driven by nonlinear colored noise. In order to overcome the difficulties caused by lack of compact Sobolev embedding on unbounded domains and weak dissipative structure of the equation, we first prove the existence, uniqueness and backward compactness of a special kind of pullback random attractor using the method of spectral decomposition in bounded domains and the uniform tail-estimates of solutions outside bounded domains over the infinite time interval. The measurability of this class of attractors is established by proving that the two classes of defined attractors are equal with respect to two different universes. Finally, the stability of the attractors is investigated by assuming that the time-dependent external forcing term converges to the time-independent external force as the time parameter tends to negative infinity.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776805","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
The modified scattering of two dimensional semi-relativistic Hartree equations 二维半相对论哈特里方程的修正散射
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-07-20 DOI: 10.1007/s00028-024-00982-7
Soonsik Kwon, Kiyeon Lee, Changhun Yang
{"title":"The modified scattering of two dimensional semi-relativistic Hartree equations","authors":"Soonsik Kwon, Kiyeon Lee, Changhun Yang","doi":"10.1007/s00028-024-00982-7","DOIUrl":"https://doi.org/10.1007/s00028-024-00982-7","url":null,"abstract":"<p>In this paper, we consider the asymptotic behaviors of small solutions to the semi-relativistic Hartree equations in two dimension. The nonlinear term is the cubic one convolved with the Coulomb potential <span>(|x|^{-1})</span>, and it produces the<i> long-range interaction</i> in the sense of scattering phenomenon. From this observation, one anticipates that small solutions converge to modified scattering states, although they decay as linear solutions. We show the global well-posedness and the modified scattering for small solutions in weighted Sobolev spaces. Our proof follows a road map of exploiting the space-time resonance by Germain et al. (Int Math Res Not 2009(3):414–432, 2008), and Pusateri (Commun Math Phys 332(3):1203–1234, 2014). Compared to the result in three dimensional case (Pusateri 2014), weaker time decay in two dimension is one of the main obstacles.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"82 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141739442","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
The viscoelastic paradox in a nonlinear Kelvin–Voigt type model of dynamic fracture 非线性开尔文-沃伊特动态断裂模型中的粘弹性悖论
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-07-08 DOI: 10.1007/s00028-024-00989-0
Maicol Caponi, Alessandro Carbotti, Francesco Sapio
{"title":"The viscoelastic paradox in a nonlinear Kelvin–Voigt type model of dynamic fracture","authors":"Maicol Caponi, Alessandro Carbotti, Francesco Sapio","doi":"10.1007/s00028-024-00989-0","DOIUrl":"https://doi.org/10.1007/s00028-024-00989-0","url":null,"abstract":"<p>In this paper, we consider a dynamic model of fracture for viscoelastic materials, in which the constitutive relation, involving the Cauchy stress and the strain tensors, is given in an implicit nonlinear form. We prove the existence of a solution to the associated viscoelastic dynamic system on a prescribed time-dependent cracked domain via a discretization-in-time argument. Moreover, we show that such a solution satisfies an energy-dissipation balance in which the energy used to increase the crack does not appear. As a consequence, in analogy to the linear case this nonlinear model exhibits the so-called <i>viscoelastic paradox</i>.\u0000</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"14 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568050","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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