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Global well-posedness of the incompressible Hall-MHD system in critical spaces 临界空间中不可压缩霍尔-MHD 系统的全局拟合性
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-01-11 DOI: 10.1007/s00028-023-00933-8
Mikihiro Fujii
{"title":"Global well-posedness of the incompressible Hall-MHD system in critical spaces","authors":"Mikihiro Fujii","doi":"10.1007/s00028-023-00933-8","DOIUrl":"https://doi.org/10.1007/s00028-023-00933-8","url":null,"abstract":"<p>In this paper, we consider the initial value problem of the incompressible Hall-MHD system and prove the global well-posedness in the scaling critical class <span>({dot{B}}_{p,infty }^{-1+frac{3}{p}}(mathbb {R}^3)times ({dot{B}}_{p,infty }^{-1+frac{3}{p}}(mathbb {R}^3) cap L^{infty }(mathbb {R}^3)))</span> for <span>(3&lt; p &lt; infty )</span>. Moreover, we also refine the smallness conditions and show that our global well-posedness holds for initial data whose <span>({dot{B}}_{p,infty }^{-1+frac{3}{p}}(mathbb {R}^3))</span>-norm is large, provided that some weaker norm is sufficiently small.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"47 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139421392","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
Rate of convergence for reaction–diffusion equations with nonlinear Neumann boundary conditions and $${mathcal {C}}^1$$ variation of the domain 具有非线性诺伊曼边界条件和 $${mathcal {C}}^1$ 域变化的反应扩散方程的收敛速率
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2024-01-11 DOI: 10.1007/s00028-023-00934-7
Marcone C. Pereira, Leonardo Pires
{"title":"Rate of convergence for reaction–diffusion equations with nonlinear Neumann boundary conditions and $${mathcal {C}}^1$$ variation of the domain","authors":"Marcone C. Pereira, Leonardo Pires","doi":"10.1007/s00028-023-00934-7","DOIUrl":"https://doi.org/10.1007/s00028-023-00934-7","url":null,"abstract":"<p>In this paper, we propose the compact convergence approach to deal with the continuity of attractors of some reaction–diffusion equations under smooth perturbations of the domain subject to nonlinear Neumann boundary conditions. We define a family of invertible linear operators to compare the dynamics of perturbed and unperturbed problems in the same phase space. All continuity arising from small smooth perturbations will be estimated by a rate of convergence given by the domain variation in a <span>({mathcal {C}}^1)</span> topology.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"41 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139461785","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
On the Weierstraß form of infinite-dimensional differential algebraic equations. 论无穷维微分代数方程的 Weierstraß 形式。
IF 1.1 3区 数学
Journal of Evolution Equations Pub Date : 2024-01-01 Epub Date: 2024-09-02 DOI: 10.1007/s00028-024-01003-3
Mehmet Erbay, Birgit Jacob, Kirsten Morris
{"title":"On the Weierstraß form of infinite-dimensional differential algebraic equations.","authors":"Mehmet Erbay, Birgit Jacob, Kirsten Morris","doi":"10.1007/s00028-024-01003-3","DOIUrl":"https://doi.org/10.1007/s00028-024-01003-3","url":null,"abstract":"<p><p>The solvability for infinite-dimensional differential algebraic equations possessing a resolvent index and a Weierstraß form is studied. In particular, the concept of integrated semigroups is used to determine a subset on which solutions exist and are unique. This information is later used for a important class of systems, namely, port-Hamiltonian differential algebraic equations.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"24 4","pages":"73"},"PeriodicalIF":1.1,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11369006/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142134393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gradient profile for the reconnection of vortex lines with the boundary in type-II superconductors II 型超导体中涡旋线与边界重新连接的梯度分布图
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2023-12-18 DOI: 10.1007/s00028-023-00932-9
Yi C. Huang, Hatem Zaag
{"title":"Gradient profile for the reconnection of vortex lines with the boundary in type-II superconductors","authors":"Yi C. Huang, Hatem Zaag","doi":"10.1007/s00028-023-00932-9","DOIUrl":"https://doi.org/10.1007/s00028-023-00932-9","url":null,"abstract":"<p>In a recent work, Duong, Ghoul and Zaag determined the gradient profile for blowup solutions of standard semilinear heat equation with power nonlinearities in the (supposed to be) generic case. Their method refines the constructive techniques introduced by Bricmont and Kupiainen and further developed by Merle and Zaag. In this paper, we extend their refinement to the problem about the reconnection of vortex lines with the boundary in a type-II superconductor under planar approximation, a physical model derived by Chapman, Hunton and Ockendon featuring the finite time quenching for the nonlinear heat equation </p><span>$$begin{aligned} frac{partial h}{partial t}=frac{partial ^2 h}{partial x^2}+e^{-h}-frac{1}{h^beta },quad beta &gt;0 end{aligned}$$</span><p>subject to initial boundary value conditions </p><span>$$begin{aligned} h(cdot ,0)=h_0&gt;0,quad h(pm 1,t)=1. end{aligned}$$</span><p>We derive the intermediate extinction profile with refined asymptotics, and with extinction time <i>T</i> and extinction point 0, the gradient profile behaves as <span>(xrightarrow 0)</span> like </p><span>$$begin{aligned} lim _{trightarrow T},(nabla h)(x,t)quad sim quad frac{1}{sqrt{2beta }}frac{x}{|x|}frac{1}{sqrt{|log |x||}} left[ frac{(beta +1)^2}{8beta }frac{|x|^2}{|log |x||}right] ^{frac{1}{beta +1}-frac{1}{2}}, end{aligned}$$</span><p>agreeing with the gradient of the extinction profile previously derived by Merle and Zaag. Our result holds with general boundary conditions and in higher dimensions.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"33 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138743641","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
Weak and parabolic solutions of advection–diffusion equations with rough velocity field 具有粗糙速度场的平流扩散方程的弱解和抛物线解
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2023-12-16 DOI: 10.1007/s00028-023-00919-6
Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa
{"title":"Weak and parabolic solutions of advection–diffusion equations with rough velocity field","authors":"Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa","doi":"10.1007/s00028-023-00919-6","DOIUrl":"https://doi.org/10.1007/s00028-023-00919-6","url":null,"abstract":"<p>We study the Cauchy problem for the advection–diffusion equation <span>(partial _t u + {{,mathrm{textrm{div}},}}(uvarvec{b}) = Delta u)</span> associated with a merely integrable divergence-free vector field <span>(varvec{b})</span> defined on the torus. We discuss existence, regularity and uniqueness results for distributional and parabolic solutions, in different regimes of integrability both for the vector field and for the initial datum. We offer an up-to-date picture of the available results scattered in the literature, and we include some original proofs. We also propose some open problems, motivated by very recent results which show ill-posedness of the equation in certain regimes of integrability via convex integration schemes.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"16 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138685646","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
Asymptotic behavior of solutions for nonlinear parabolic problems with Marcinkiewicz data 具有Marcinkiewicz数据的非线性抛物型问题解的渐近性质
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2023-11-28 DOI: 10.1007/s00028-023-00929-4
Lucio Boccardo, Luigi Orsina, Maria Michaela Porzio
{"title":"Asymptotic behavior of solutions for nonlinear parabolic problems with Marcinkiewicz data","authors":"Lucio Boccardo, Luigi Orsina, Maria Michaela Porzio","doi":"10.1007/s00028-023-00929-4","DOIUrl":"https://doi.org/10.1007/s00028-023-00929-4","url":null,"abstract":"<p>In this paper we prove the asymptotic behavior, as <i>t</i> tends to zero, of solutions of nonlinear parabolic equations with initial data belonging to Marcinkiewicz spaces. Namely, that if the initial datum <span>(u_{0})</span> belongs to <span>(M^{m}(Omega ))</span>, then </p><span>$$begin{aligned} Vert u(t)Vert _{scriptstyle L^{r}(Omega )}^{*} le {mathcal {C}},frac{Vert u_{0}Vert _{scriptstyle L^{m}(Omega )}^{*}}{t^{frac{N}{2}left( frac{1}{m} - frac{1}{r}right) }}, qquad forall ,t &gt; 0, end{aligned}$$</span><p>thus extending to Marcinkiewicz spaces the results which hold for data in Lebesgue spaces.\u0000</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"33 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138518585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Temporal regularity of the solution to the incompressible Euler equations in the end-point critical Triebel–Lizorkin space $$F^{d+1}_{1, infty }(mathbb {R}^d)$$ 端点临界triiebel - lizorkin空间中不可压缩欧拉方程解的时间正则性 $$F^{d+1}_{1, infty }(mathbb {R}^d)$$
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2023-11-28 DOI: 10.1007/s00028-023-00927-6
Hee Chul Pak
{"title":"Temporal regularity of the solution to the incompressible Euler equations in the end-point critical Triebel–Lizorkin space $$F^{d+1}_{1, infty }(mathbb {R}^d)$$","authors":"Hee Chul Pak","doi":"10.1007/s00028-023-00927-6","DOIUrl":"https://doi.org/10.1007/s00028-023-00927-6","url":null,"abstract":"<p>An evidence of temporal discontinuity of the solution in <span>(F^s_{1, infty }(mathbb {R}^d))</span> is presented, which implies the ill-posedness of the Cauchy problem for the Euler equations. Continuity and weak-type continuity of the solutions in related spaces are also discussed.\u0000</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"90 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138515707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a quasilinear fully parabolic predator–prey model with indirect pursuit-evasion interaction 一类具有追捕-逃避间接相互作用的拟线性全抛物型捕食者-猎物模型
IF 1.4 3区 数学
Journal of Evolution Equations Pub Date : 2023-11-28 DOI: 10.1007/s00028-023-00931-w
Chuanjia Wan, Pan Zheng, Wenhai Shan
{"title":"On a quasilinear fully parabolic predator–prey model with indirect pursuit-evasion interaction","authors":"Chuanjia Wan, Pan Zheng, Wenhai Shan","doi":"10.1007/s00028-023-00931-w","DOIUrl":"https://doi.org/10.1007/s00028-023-00931-w","url":null,"abstract":"<p>In this paper, we study the quasilinear fully parabolic predator–prey model with indirect pursuit-evasion interaction </p><span>$$begin{aligned} begin{aligned} left{ begin{aligned}&amp;u_t=nabla cdot left( D_{1}(u)nabla uright) -chi nabla cdot left( S_{1}(u)nabla zright) +uleft( alpha v-a_{1} -b_{1}uright) ,&amp;x in varOmega , t&gt;0, &amp;v_t=nabla cdot left( D_{2}(v)nabla vright) +xi nabla cdot left( S_{2}(v)nabla {w}right) +vleft( a_{2} -b_{2} v-uright) ,&amp;x in varOmega , t&gt;0, &amp;{w_t}=Delta w+beta {u}-gamma {w},&amp;x in varOmega , t&gt;0,&amp;{z_t}=Delta z+delta {v}-rho z,&amp;x in varOmega , t&gt;0, end{aligned} right. end{aligned} end{aligned}$$</span><p>under homogeneous Neumann boundary conditions in a smoothly bounded domain <span>(varOmega subset mathbb {R}^{n}(nge 1))</span>, where <span>( chi , xi , alpha , beta , gamma , delta , rho , a_{1},a_{2},)</span> <span>(b_{1},b_{2})</span> are positive parameters, the functions <span>(D_{i} in C^{2}([0,infty )))</span> and <span>(S_{i}in C^{2}([0,infty )))</span> with <span>(S_{i}(0)=0(i=1,2))</span>. Firstly, under certain suitable conditions, we prove that the system admits a unique globally bounded classical solution when <span>(nle 4)</span>. Moreover, we investigate the asymptotic stability and precise convergence rates of globally bounded solutions by constructing appropriate Lyapunov functionals. Finally, we present numerical simulations that not only support our theoretical results, but also involve new and interesting phenomena.</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":"77 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138542749","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 pathwise regularization by noise phenomenon for the evolutionary p-Laplace equation 演化p-拉普拉斯方程的噪声现象路径正则化
3区 数学
Journal of Evolution Equations Pub Date : 2023-11-09 DOI: 10.1007/s00028-023-00926-7
Florian Bechtold, Jörn Wichmann
{"title":"A pathwise regularization by noise phenomenon for the evolutionary p-Laplace equation","authors":"Florian Bechtold, Jörn Wichmann","doi":"10.1007/s00028-023-00926-7","DOIUrl":"https://doi.org/10.1007/s00028-023-00926-7","url":null,"abstract":"Abstract We study an evolutionary p -Laplace problem whose potential is subject to a translation in time. Provided the trajectory along which the potential is translated admits a sufficiently regular local time, we establish existence of solutions to the problem for singular potentials for which a priori bounds in classical approaches break down, thereby establishing a pathwise regularization by noise phenomena for this nonlinear problem.","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":" 11","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135192783","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: 3
Boundedness of the conformal hyperboloidal energy for a wave-Klein–Gordon model 波-克莱因-戈登模型共形双曲能量的有界性
3区 数学
Journal of Evolution Equations Pub Date : 2023-11-09 DOI: 10.1007/s00028-023-00925-8
Philippe G. LeFloch, Jesús Oliver, Yoshio Tsutsumi
{"title":"Boundedness of the conformal hyperboloidal energy for a wave-Klein–Gordon model","authors":"Philippe G. LeFloch, Jesús Oliver, Yoshio Tsutsumi","doi":"10.1007/s00028-023-00925-8","DOIUrl":"https://doi.org/10.1007/s00028-023-00925-8","url":null,"abstract":"","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":" 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135241265","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: 2
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