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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
Stability via closure relations with applications to dissipative and port-Hamiltonian systems 通过闭合关系实现稳定性，并应用于耗散系统和端口-哈密尔顿系统
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-07-05 DOI: 10.1007/s00028-024-00992-5
Jochen Glück, Birgit Jacob, Annika Meyer, Christian Wyss, Hans Zwart
{"title":"Stability via closure relations with applications to dissipative and port-Hamiltonian systems","authors":"Jochen Glück, Birgit Jacob, Annika Meyer, Christian Wyss, Hans Zwart","doi":"10.1007/s00028-024-00992-5","DOIUrl":"https://doi.org/10.1007/s00028-024-00992-5","url":null,"abstract":"<p>We consider differential operators <i>A</i> that can be represented by means of a so-called closure relation in terms of a simpler operator <span>(A_{{text {ext}}})</span> defined on a larger space. We analyse how the spectral properties of <i>A</i> and <span>(A_{{text {ext}}})</span> are related and give sufficient conditions for exponential stability of the semigroup generated by <i>A</i> in terms of the semigroup generated by <span>(A_{{text {ext}}})</span>. As applications we study the long-term behaviour of a coupled wave–heat system on an interval, parabolic equations on bounded domains that are coupled by matrix-valued potentials, and of linear infinite-dimensional port-Hamiltonian systems with dissipation on an interval.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"27 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547599","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 existence and scattering for the inhomogeneous nonlinear Schrödinger equation 非均质非线性薛定谔方程的全局存在性和散射
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-07-05 DOI: 10.1007/s00028-024-00965-8
Lassaad Aloui, Slim Tayachi
{"title":"Global existence and scattering for the inhomogeneous nonlinear Schrödinger equation","authors":"Lassaad Aloui, Slim Tayachi","doi":"10.1007/s00028-024-00965-8","DOIUrl":"https://doi.org/10.1007/s00028-024-00965-8","url":null,"abstract":"<p>In this paper, we consider the inhomogeneous nonlinear Schrödinger equation <span>(ipartial _t u +Delta u =K(x)|u|^alpha u,; u(0)=u_0in H^1({mathbb {R}}^N),; Nge 3,; |K(x)|+|x||nabla K(x)|lesssim |x|^{-b},; 0&lt;b&lt; min (2, N-2),; 0&lt;alpha &lt;{(4-2b)/(N-2)})</span>. We obtain novel results of global existence for oscillating initial data and scattering theory in a weighted <span>(L^2)</span>-space for a new range <span>(alpha _0(b)&lt;alpha &lt;(4-2b)/N)</span>. The value <span>(alpha _0(b))</span> is the positive root of <span>(Nalpha ^2+(N-2+2b)alpha -4+2b=0,)</span> which extends the Strauss exponent known for <span>(b=0)</span>. Our results improve the known ones for <span>(K(x)=mu |x|^{-b})</span>, <span>(mu in {mathbb {C}})</span>. For general potentials, we highlight the impact of the behavior at the origin and infinity on the allowed range of <span>(alpha )</span>. In the defocusing case, we prove decay estimates provided that the potential satisfies some rigidity-type condition which leads to a scattering result. We give also a new scattering criterion taking into account the potential <i>K</i>.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"23 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547598","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
Local and global strong solutions to the 3D Navier–Stokes equations with damping 带阻尼的三维纳维-斯托克斯方程的局部和全局强解
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-07-05 DOI: 10.1007/s00028-024-00987-2
Kwang-Ok Li, Yong-Ho Kim, Yong-Nam Kim, Sung-Il O
{"title":"Local and global strong solutions to the 3D Navier–Stokes equations with damping","authors":"Kwang-Ok Li, Yong-Ho Kim, Yong-Nam Kim, Sung-Il O","doi":"10.1007/s00028-024-00987-2","DOIUrl":"https://doi.org/10.1007/s00028-024-00987-2","url":null,"abstract":"<p>This paper studies regularity properties of the weak solutions to the 3D Navier–Stokes equations with damping in the whole space and bounded domains. We find the space restriction on the initial velocity to guarantee the local existence of strong solutions. Based on it, we complete the existence results for the global strong solutions in the whole space and improve the restriction on the damping exponent for the existence of the global strong solutions in the bounded domains.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"29 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547597","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
Existence and convergence of the length-preserving elastic flow of clamped curves 夹紧曲线的保长弹性流的存在性和收敛性
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-07-02 DOI: 10.1007/s00028-024-00988-1
Fabian Rupp, Adrian Spener
{"title":"Existence and convergence of the length-preserving elastic flow of clamped curves","authors":"Fabian Rupp, Adrian Spener","doi":"10.1007/s00028-024-00988-1","DOIUrl":"https://doi.org/10.1007/s00028-024-00988-1","url":null,"abstract":"<p>We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative <span>(L^2)</span>-gradient flow of the elastic energy. For any initial curve lying merely in the energy space we show existence and parabolic smoothing of the solution. Applying previous results on long-time existence and proving a constrained Łojasiewicz–Simon gradient inequality we furthermore show convergence to a critical point as time tends to infinity.\u0000</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"16 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526882","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
Algebraic decay rates for 3D Navier–Stokes and Navier–Stokes–Coriolis equations in $$ dot{H}^{frac{1}{2}}$$ 三维纳维-斯托克斯方程和纳维-斯托克斯-科里奥利方程在 $$ dot{H}^{frac{1}{2}}$ 中的代数衰减率
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-06-29 DOI: 10.1007/s00028-024-00991-6
Masahiro Ikeda, Leonardo Kosloff, César J. Niche, Gabriela Planas
{"title":"Algebraic decay rates for 3D Navier–Stokes and Navier–Stokes–Coriolis equations in $$ dot{H}^{frac{1}{2}}$$","authors":"Masahiro Ikeda, Leonardo Kosloff, César J. Niche, Gabriela Planas","doi":"10.1007/s00028-024-00991-6","DOIUrl":"https://doi.org/10.1007/s00028-024-00991-6","url":null,"abstract":"<p>An algebraic upper bound for the decay rate of solutions to the Navier–Stokes and Navier–Stokes–Coriolis equations in the critical space <span>(dot{H} ^{frac{1}{2}} (mathbb {R}^3))</span> is derived using the Fourier splitting method. Estimates are framed in terms of the decay character of initial data, leading to solutions with algebraic decay and showing in detail the roles played by the linear and nonlinear parts. The proof is carried on purely in the critical space, as no <span>(L^2 (mathbb {R}^3))</span> estimates are available for the solution. This is the first instance in which such a method is used for obtaining decay bounds in a critical space for a nonlinear equation.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"122 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503813","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
An interpolation inequality and its applications to stability of fractional resolvent families 插值不等式及其在分数解析族稳定性中的应用
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-06-28 DOI: 10.1007/s00028-024-00990-7
Jie Mei, Miao Li
{"title":"An interpolation inequality and its applications to stability of fractional resolvent families","authors":"Jie Mei, Miao Li","doi":"10.1007/s00028-024-00990-7","DOIUrl":"https://doi.org/10.1007/s00028-024-00990-7","url":null,"abstract":"<p>In this paper, we prove an interpolation inequality on Riemann–Liouville fractional integrals and then use it to study the strong stability and semi-uniform stability of fractional resolvent families of order <span>(0&lt;alpha &lt;2)</span>. Let <i>A</i> denote the generator of a bounded fractional resolvent family. We show that if <span>(sigma (A)cap (textrm{i}{mathbb {R}})^alpha )</span> is countable and <span>(sigma _r(A) cap (textrm{i}{mathbb {R}})^alpha =varnothing )</span>, then the bounded fractional resolvent family is strongly stable. And the semi-uniform stability of the fractional resolvent family is equivalent to <span>(sigma (A)cap (textrm{i}{mathbb {R}})^alpha =varnothing )</span>. Moreover, the relation between decay rates of semi-uniform stability and growth of the resolvent of <i>A</i> along <span>((textrm{i}{mathbb {R}})^alpha )</span> is given.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"10 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503816","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 rotating liquid drops with surface tension 具有表面张力的旋转液滴的稳定性
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-06-25 DOI: 10.1007/s00028-024-00986-3
Keiichi Watanabe
{"title":"Stability of rotating liquid drops with surface tension","authors":"Keiichi Watanabe","doi":"10.1007/s00028-024-00986-3","DOIUrl":"https://doi.org/10.1007/s00028-024-00986-3","url":null,"abstract":"<p>The aim of this paper is to investigate the stability of a stationary solution of free boundary problems of the incompressible Navier–Stokes equations in a three-dimensional bounded domain with surface tension. More precisely, this article proves that if the initial angular momentum is sufficiently small and if the initial configuration is sufficiently close to equilibrium, then there exists a global classical solution that converges exponentially fast to a uniform rigid rotation of the liquid as <span>(t rightarrow infty )</span> with respect to a certain axis. The proof of the <i>unique</i> existence of a stationary solution is also given.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"83 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503815","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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