Journal of Evolution Equations最新文献

{"title":"Stability estimates for semigroups in the Banach case","authors":"","doi":"10.1007/s00028-024-00958-7","DOIUrl":"https://doi.org/10.1007/s00028-024-00958-7","url":null,"abstract":"<h3>Abstract</h3> <p>The purpose of this paper is to revisit previous works of the author with Helffer and Sjöstrand (arXiv:1001.4171v1. 2010; Int Equ Op Theory 93(3):36, 2021) on the stability of semigroups which were proved in the Hilbert case by considering the Banach case at the light of a paper by Latushkin and Yurov (Discrete Contin Dyn Syst 33:5203–5216, 2013).</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"82 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156507","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":"Remarks on uniqueness and energy conservation for electron-MHD system","authors":"Fan Wu","doi":"10.1007/s00028-024-00955-w","DOIUrl":"https://doi.org/10.1007/s00028-024-00955-w","url":null,"abstract":"<p>This paper is concerned with the uniqueness and energy conservation of weak solutions for Electron-MHD system. Under suitable assumptions, we first show that the Electron-MHD system has a unique weak solution. In addition, we show that weak solution conserves energy if <span>(nabla times bin L^2(0, T; L^4({mathbb {R}}^d))(dge 2))</span> or <span>( nabla times b in L^{frac{4d+8}{d+4}}left( 0, T; L^{frac{4d+8}{d+4}}({mathbb {R}}^{d})right) (d=2, 3, 4))</span>.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"38 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140153454","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":"A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects","authors":"Christian Stinner, Michael Winkler","doi":"10.1007/s00028-024-00954-x","DOIUrl":"https://doi.org/10.1007/s00028-024-00954-x","url":null,"abstract":"<p>The quasilinear Keller–Segel system </p><span>$$begin{aligned} left{ begin{array}{l} u_t=nabla cdot (D(u)nabla u) - nabla cdot (S(u)nabla v), v_t=Delta v-v+u, end{array}right. end{aligned}$$</span><p>endowed with homogeneous Neumann boundary conditions is considered in a bounded domain <span>(Omega subset {mathbb {R}}^n)</span>, <span>(n ge 3)</span>, with smooth boundary for sufficiently regular functions <i>D</i> and <i>S</i> satisfying <span>(D&gt;0)</span> on <span>([0,infty ))</span>, <span>(S&gt;0)</span> on <span>((0,infty ))</span> and <span>(S(0)=0)</span>. On the one hand, it is shown that if <span>(frac{S}{D})</span> satisfies the subcritical growth condition </p><span>$$begin{aligned} frac{S(s)}{D(s)} le C s^alpha qquad text{ for } text{ all } sge 1 qquad text{ with } text{ some } alpha &lt; frac{2}{n} end{aligned}$$</span><p>and <span>(C&gt;0)</span>, then for any sufficiently regular initial data there exists a global weak energy solution such that <span>({ mathrm{{ess}}} sup _{t&gt;0} Vert u(t) Vert _{L^p(Omega )}&lt;infty )</span> for some <span>(p &gt; frac{2n}{n+2})</span>. On the other hand, if <span>(frac{S}{D})</span> satisfies the supercritical growth condition </p><span>$$begin{aligned} frac{S(s)}{D(s)} ge c s^alpha qquad text{ for } text{ all } sge 1 qquad text{ with } text{ some } alpha &gt; frac{2}{n} end{aligned}$$</span><p>and <span>(c&gt;0)</span>, then the nonexistence of a global weak energy solution having the boundedness property stated above is shown for some initial data in the radial setting. This establishes some criticality of the value <span>(alpha = frac{2}{n})</span> for <span>(n ge 3)</span>, without any additional assumption on the behavior of <i>D</i>(<i>s</i>) as <span>(s rightarrow infty )</span>, in particular without requiring any algebraic lower bound for <i>D</i>. When applied to the Keller–Segel system with volume-filling effect for probability distribution functions of the type <span>(Q(s) = exp (-s^beta ))</span>, <span>(s ge 0)</span>, for global solvability the exponent <span>(beta = frac{n-2}{n})</span> is seen to be critical.\u0000</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"102 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140153456","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":"Nonlinear partial differential equations on noncommutative Euclidean spaces","authors":"","doi":"10.1007/s00028-023-00928-5","DOIUrl":"https://doi.org/10.1007/s00028-023-00928-5","url":null,"abstract":"<h3>Abstract</h3> <p>Noncommutative Euclidean spaces—otherwise known as Moyal spaces or quantum Euclidean spaces—are a standard example of a non-compact noncommutative geometry. Recent progress in the harmonic analysis of these spaces gives us the opportunity to highlight some of their peculiar features. For example, the theory of nonlinear partial differential equations has unexpected properties in this noncommutative setting. We develop elementary aspects of paradifferential calculus for noncommutative Euclidean spaces and give some applications to nonlinear evolution equations. We demonstrate how the analysis of some equations radically simplifies in the strictly noncommutative setting.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"35 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139969312","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":"Well-posedness and longtime dynamics for the finitely degenerate parabolic and pseudo-parabolic equations","authors":"Gongwei Liu, Shuying Tian","doi":"10.1007/s00028-024-00945-y","DOIUrl":"https://doi.org/10.1007/s00028-024-00945-y","url":null,"abstract":"<p>We consider the initial-boundary value problem for degenerate parabolic and pseudo-parabolic equations associated with Hörmander-type operator. Under the subcritical growth restrictions on the nonlinearity <i>f</i>(<i>u</i>), which are determined by the generalized Métivier index, we establish the global existence of solutions and the corresponding attractors. Finally, we show the upper semicontinuity of the attractors in the topology of <span>(H_{X,0}^1(Omega ))</span>.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"19 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139969814","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":"Homogeneous Sobolev global-in-time maximal regularity and related trace estimates","authors":"Anatole Gaudin","doi":"10.1007/s00028-024-00946-x","DOIUrl":"https://doi.org/10.1007/s00028-024-00946-x","url":null,"abstract":"<p>In this paper, we prove global-in-time <span>(dot{textrm{H}}^{alpha ,q})</span>-maximal regularity for a class of injective, but not invertible, sectorial operators on a UMD Banach space <i>X</i>, provided <span>(qin (1,+infty ))</span>, <span>(alpha in (-1+1/q,1/q))</span>. We also prove the corresponding trace estimate, so that the solution to the canonical abstract Cauchy problem is continuous with values in a not necessarily complete trace space. In order to put our result in perspective, we also provide a short review on <span>(textrm{L}^q)</span>-maximal regularity which includes some recent advances such as the revisited homogeneous operator and interpolation theory by Danchin, Hieber, Mucha and Tolksdorf. This theory will be used to build the appropriate trace space, from which we want to choose the initial data, and the solution of our abstract Cauchy problem to fall in.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"80 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757623","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":"Long time behavior of solutions of an electroconvection model in $${mathbb {R}}^2$$","authors":"","doi":"10.1007/s00028-024-00944-z","DOIUrl":"https://doi.org/10.1007/s00028-024-00944-z","url":null,"abstract":"<h3>Abstract</h3> <p>We consider a two dimensional electroconvection model which consists of a nonlinear and nonlocal system coupling the evolutions of a charge distribution and a fluid. We show that the solutions decay in time in <span> <span>(L^2({{mathbb {R}}}^2))</span> </span> at the same sharp rate as the linear uncoupled system. This is achieved by proving that the difference between the nonlinear and linear evolution decays at a faster rate than the linear evolution. In order to prove the sharp <span> <span>(L^2)</span> </span> decay we establish bounds for decay in <span> <span>(H^2({{mathbb {R}}}^2))</span> </span> and a logarithmic growth in time of a quadratic moment of the charge density.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"66 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757334","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":"Existence of a weak solution and blow-up of strong solutions for a two-component Fornberg–Whitham system","authors":"Zhihao Bai, Yang Wang, Long Wei","doi":"10.1007/s00028-023-00941-8","DOIUrl":"https://doi.org/10.1007/s00028-023-00941-8","url":null,"abstract":"<p>In this paper, we investigate the existence of a weak solution and blow-up of strong solutions to a two-component Fornberg–Whitham system. Due to the absence of some useful conservation laws, we establish the existence of a weak solution to the system in lower order Sobolev spaces <span>(H^{s}times H^{s-1})</span> (<span>(sin (1,3/2])</span>) via a modified pseudo-parabolic regularization method. And then, a blow-up scenario for strong solutions to this system is shown. By the analysis of Riccati-type inequalities recently, we present some sufficient conditions on the initial data that lead to the blow-up for corresponding strong solutions to the system.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"45 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757335","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":"Well-posedness and asynchronous exponential growth of an age-weighted structured fish population model with diffusion in $$L^1$$","authors":"Samir Boujijane, Said Boulite, Mohamed Halloumi, Lahcen Maniar, Abdelaziz Rhandi","doi":"10.1007/s00028-023-00942-7","DOIUrl":"https://doi.org/10.1007/s00028-023-00942-7","url":null,"abstract":"<p>In the present paper, we address the asymptotic behavior of a fish population system structured in age and weight, while also incorporating spatial effects. Initially, we develop an abstract perturbation result concerning the essential spectral radius, employing the regular systems approach. Following that, we present the model in the form of a perturbed boundary problem, which involves unbounded operators on the boundary. Using time-invariant regular techniques, we construct the corresponding semigroup solution. Then, we designate an operator characteristic equation of the primary system via the radius of a bounded linear operator defined on the boundary space. Moreover, we provide a characterization of the uniform exponential stability and the asynchronous exponential growth property (AEG) by localizing the essential radius and proving the irreducibility of the perturbed semigroup. Finally, we precise the projection that emerged from the (AEG) property; this depends on the developed characteristic equation.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"66 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757516","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 a thermodynamically consistent model for magnetoviscoelastic fluids in 3D","authors":"Hengrong Du, Yuanzhen Shao, Gieri Simonett","doi":"10.1007/s00028-023-00938-3","DOIUrl":"https://doi.org/10.1007/s00028-023-00938-3","url":null,"abstract":"<p>We introduce a system of equations that models a non-isothermal magnetoviscoelastic fluid. We show that the model is thermodynamically consistent, and that the critical points of the entropy functional with prescribed energy correspond exactly with the equilibria of the system. The system is investigated in the framework of quasilinear parabolic systems and shown to be locally well-posed in an <span>(L_p)</span>-setting. Furthermore, we prove that constant equilibria are normally stable. In particular, we show that solutions that start close to a constant equilibrium exist globally and converge exponentially fast to a (possibly different) constant equilibrium. Finally, we establish that the negative entropy serves as a strict Lyapunov functional and we then show that every solution that is eventually bounded in the topology of the natural state space exists globally and converges to the set of equilibria.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"5 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139757306","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}