Annals of Pde最新文献_第4页

A Fully Nonlinear Degenerate Free Transmission Problem 全非线性退化自由传输问题

IF 2.4 1区数学

Annals of Pde Pub Date : 2024-02-20 DOI: 10.1007/s40818-024-00168-x

Gerardo Huaroto, Edgard A. Pimentel, Giane C. Rampasso, Andrzej Święch

引用次数: 0

Existence and Regularity for Prescribed Lorentzian Mean Curvature Hypersurfaces, and the Born–Infeld Model 规定洛伦兹平均曲率超曲面的存在性和正则性，以及玻恩-英菲尔德模型

IF 2.4 1区数学

Annals of Pde Pub Date : 2024-01-29 DOI: 10.1007/s40818-023-00167-4

Jaeyoung Byeon, Norihisa Ikoma, Andrea Malchiodi, Luciano Mari

{"title":"Existence and Regularity for Prescribed Lorentzian Mean Curvature Hypersurfaces, and the Born–Infeld Model","authors":"Jaeyoung Byeon, Norihisa Ikoma, Andrea Malchiodi, Luciano Mari","doi":"10.1007/s40818-023-00167-4","DOIUrl":"10.1007/s40818-023-00167-4","url":null,"abstract":"<div><p>Given a measure <span>(rho )</span> on a domain <span>(Omega subset {mathbb {R}}^m)</span>, we study spacelike graphs over <span>(Omega )</span> in Minkowski space with Lorentzian mean curvature <span>(rho )</span> and Dirichlet boundary condition on <span>(partial Omega )</span>, which solve </p><div><figure><div><div><picture><img></picture></div></div></figure></div><p> The graph function also represents the electric potential generated by a charge <span>(rho )</span> in electrostatic Born-Infeld’s theory. Even though there exists a unique minimizer <span>(u_rho )</span> of the associated action </p><div><div><span>$$begin{aligned} I_rho (psi ) doteq int _{Omega } Big ( 1 - sqrt{1-|Dpsi |^2} Big ) textrm{d}x - langle rho , psi rangle end{aligned}$$</span></div></div><p>among functions <span>(psi )</span> satisfying <span>(|Dpsi | le 1)</span>, by the lack of smoothness of the Lagrangian density for <span>(|Dpsi | = 1)</span> one cannot guarantee that <span>(u_rho )</span> satisfies the Euler-Lagrange equation (<span>(mathcal{B}mathcal{I})</span>). A chief difficulty comes from the possible presence of light segments in the graph of <span>(u_rho )</span>. In this paper, we investigate the existence of a solution for general <span>(rho )</span>. In particular, we give sufficient conditions to guarantee that <span>(u_rho )</span> solves (<span>(mathcal{B}mathcal{I})</span>) and enjoys <span>(log )</span>-improved energy and <span>(W^{2,2}_textrm{loc})</span> estimate. Furthermore, we construct examples which suggest a sharp threshold for the regularity of <span>(rho )</span> to ensure the solvability of (<span>(mathcal{B}mathcal{I})</span>).</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 for perturbations of the 2D stochastic Navier–Stokes equations with space-time white noise 带有时空白噪声的二维随机纳维-斯托克斯方程扰动的全局存在性

IF 2.8 1区数学

Annals of Pde Pub Date : 2023-12-27 DOI: 10.1007/s40818-023-00165-6

Martin Hairer, Tommaso Rosati

{"title":"Global existence for perturbations of the 2D stochastic Navier–Stokes equations with space-time white noise","authors":"Martin Hairer, Tommaso Rosati","doi":"10.1007/s40818-023-00165-6","DOIUrl":"10.1007/s40818-023-00165-6","url":null,"abstract":"<div><p>We prove global in time well-posedness for perturbations of the 2D stochastic Navier–Stokes equations </p><div><div><span>$$begin{aligned} partial _t u + u cdot nabla u= & {} Delta u - nabla p + zeta + xi ;, qquad u (0, cdot ) = u_{0} ;, {text {div}}(u)= & {} 0 ;, end{aligned}$$</span></div></div><p>driven by additive space-time white noise <span>( xi )</span>, with perturbation <span>( zeta )</span> in the Hölder–Besov space <span>(mathcal {C}^{-2 + 3kappa } )</span>, periodic boundary conditions and initial condition <span>( u_{0} in mathcal {C}^{-1 + kappa } )</span> for any <span>( kappa >0 )</span>. The proof relies on an energy estimate which in turn builds on a dynamic high-low frequency decomposition and tools from paracontrolled calculus. Our argument uses that the solution to the linear equation is a <span>( log )</span>–correlated field, yielding a double exponential growth bound on the solution. Notably, our method does not rely on any explicit knowledge of the invariant measure to the SPDE, hence the perturbation <span>( zeta )</span> is not restricted to the Cameron–Martin space of the noise, and the initial condition may be anticipative. Finally, we introduce a notion of weak solution that leads to well-posedness for all initial data <span>( u_{0})</span> in <span>( L^{2} )</span>, the critical space of initial conditions.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-023-00165-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139050689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Nonlinear Landau Damping for the Vlasov–Poisson System in (mathbb {R}^3): The Poisson Equilibrium (mathbb {R}^3) 中弗拉索夫-泊松系统的非线性朗道阻尼：泊松均衡

IF 2.8 1区数学

Annals of Pde Pub Date : 2023-12-13 DOI: 10.1007/s40818-023-00161-w

Alexandru D. Ionescu, Benoit Pausader, Xuecheng Wang, Klaus Widmayer

引用次数: 0

Time Periodic Solutions Close to Localized Radial Monotone Profiles for the 2D Euler Equations 接近二维欧拉方程局部径向单调剖面的时间周期解

IF 2.8 1区数学

Annals of Pde Pub Date : 2023-12-12 DOI: 10.1007/s40818-023-00166-5

Claudia García, Taoufik Hmidi, Joan Mateu

{"title":"Time Periodic Solutions Close to Localized Radial Monotone Profiles for the 2D Euler Equations","authors":"Claudia García, Taoufik Hmidi, Joan Mateu","doi":"10.1007/s40818-023-00166-5","DOIUrl":"10.1007/s40818-023-00166-5","url":null,"abstract":"<div><p>In this paper, we address for the 2D Euler equations the existence of rigid time periodic solutions close to stationary radial vortices of type <span>(f_0(|x|)textbf{1}_{{{,mathrm{mathbb {D}},}}}(x))</span>, with <span>({{,mathrm{mathbb {D}},}})</span> the unit disc and <span>(f_0)</span> being a strictly monotonic profile with constant sign. We distinguish two scenarios according to the sign of the profile: <i>defocusing and focusing.</i> In the first regime, we have scarcity of the bifurcating curves associated with lower symmetry. However in the <i>focusing case</i> we get a countable family of bifurcating solutions associated with large symmetry. The approach developed in this work is new and flexible, and the explicit expression of the radial profile is no longer required as in [41] with the quadratic shape. The alternative for that is a refined study of the associated spectral problem based on Sturm-Liouville differential equation with a variable potential that changes the sign depending on the shape of the profile and the location of the time period. Deep hidden structure on positive definiteness of some intermediate integral operators are also discovered and used in a crucial way. Notice that a special study will be performed for the linear problem associated with the first mode founded on Prüfer transformation and Kneser’s Theorem on the non-oscillation phenomenon.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"10 1","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138822346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 local well-posedness for the relativistic Euler equations for a liquid body 液体相对论欧拉方程的局部适定性

IF 2.8 1区数学

Annals of Pde Pub Date : 2023-12-01 DOI: 10.1007/s40818-023-00164-7

Daniel Ginsberg, Hans Lindblad

引用次数: 2

Instability of Gravitational and Electromagnetic Perturbations of Extremal Reissner–Nordström Spacetime 极端时空的引力和电磁扰动的不稳定性Reissner-Nordström

IF 2.8 1区数学

Annals of Pde Pub Date : 2023-11-17 DOI: 10.1007/s40818-023-00158-5

Marios Antonios Apetroaie

{"title":"Instability of Gravitational and Electromagnetic Perturbations of Extremal Reissner–Nordström Spacetime","authors":"Marios Antonios Apetroaie","doi":"10.1007/s40818-023-00158-5","DOIUrl":"10.1007/s40818-023-00158-5","url":null,"abstract":"<div><p>We study the linear stability problem to gravitational and electromagnetic perturbations of the <i>extremal</i>, <span>( |Q|=M, )</span> Reissner–Nordström spacetime, as a solution to the Einstein–Maxwell equations. Our work uses and extends the framework [28, 32] of Giorgi, and contrary to the subextremal case we prove that instability results hold for a set of gauge invariant quantities along the event horizon <span>( {mathcal {H}}^+ )</span>. In particular, for associated quantities shown to satisfy generalized Regge–Wheeler equations we prove decay, non-decay, and polynomial blow-up estimates asymptotically along <span>( {mathcal {H}}^+ )</span>, the exact behavior depending on the number of translation invariant derivatives that we take. As a consequence, we show that for generic initial data, solutions to the generalized Teukolsky system of positive and negative spin satisfy both stability and instability results. It is worth mentioning that the negative spin solutions are significantly more unstable, with the extreme curvature component <span>( {underline{alpha }} )</span> not decaying asymptotically along the event horizon <span>( {mathcal {H}}^+, )</span> a result previously unknown in the literature.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"9 2","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-023-00158-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138138512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Anomalous Dissipation and Lack of Selection in the Obukhov–Corrsin Theory of Scalar Turbulence Obukhov-Corrsin标量湍流理论中的异常耗散和缺乏选择。

IF 2.8 1区数学

Annals of Pde Pub Date : 2023-11-02 DOI: 10.1007/s40818-023-00162-9

Maria Colombo, Gianluca Crippa, Massimo Sorella

{"title":"Anomalous Dissipation and Lack of Selection in the Obukhov–Corrsin Theory of Scalar Turbulence","authors":"Maria Colombo, Gianluca Crippa, Massimo Sorella","doi":"10.1007/s40818-023-00162-9","DOIUrl":"10.1007/s40818-023-00162-9","url":null,"abstract":"<div><p>The Obukhov–Corrsin theory of scalar turbulence [21, 54] advances quantitative predictions on passive-scalar advection in a turbulent regime and can be regarded as the analogue for passive scalars of Kolmogorov’s K41 theory of fully developed turbulence [47]. The scaling analysis of Obukhov and Corrsin from 1949 to 1951 identifies a critical regularity threshold for the advection-diffusion equation and predicts anomalous dissipation in the limit of vanishing diffusivity in the supercritical regime. In this paper we provide a fully rigorous mathematical validation of this prediction by constructing a velocity field and an initial datum such that the unique bounded solution of the advection-diffusion equation is bounded uniformly-in-diffusivity within any fixed supercritical Obukhov-Corrsin regularity regime while also exhibiting anomalous dissipation. Our approach relies on a fine quantitative analysis of the interaction between the spatial scale of the solution and the scale of the Brownian motion which represents diffusion in a stochastic Lagrangian setting. This provides a direct Lagrangian approach to anomalous dissipation which is fundamental in order to get detailed insight on the behavior of the solution. Exploiting further this approach, we also show that for a velocity field in <span>(C^alpha )</span> of space and time (for an arbitrary <span>(0 le alpha < 1)</span>) neither vanishing diffusivity nor regularization by convolution provide a selection criterion for bounded solutions of the advection equation. This is motivated by the fundamental open problem of the selection of solutions of the Euler equations as vanishing-viscosity limit of solutions of the Navier-Stokes equations and provides a complete negative answer in the case of passive advection.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"9 2","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10622394/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71486919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 15

Orientation Mixing in Active Suspensions 活性悬浮液中的定向混合

IF 2.8 1区数学

Annals of Pde Pub Date : 2023-10-20 DOI: 10.1007/s40818-023-00163-8

Michele Coti Zelati, Helge Dietert, David Gérard-Varet

{"title":"Orientation Mixing in Active Suspensions","authors":"Michele Coti Zelati, Helge Dietert, David Gérard-Varet","doi":"10.1007/s40818-023-00163-8","DOIUrl":"10.1007/s40818-023-00163-8","url":null,"abstract":"<div><p>We study a popular kinetic model introduced by Saintillan and Shelley for the dynamics of suspensions of active elongated particles where the particles are described by a distribution in space and orientation. The uniform distribution of particles is the stationary state of incoherence which is known to exhibit a phase transition. We perform an extensive study of the linearised evolution around the incoherent state. We show (i) in the non-diffusive regime corresponding to spectral (neutral) stability that the suspensions experience a mixing phenomenon similar to Landau damping and we provide optimal pointwise in time decay rates in weak topology. Further, we show (ii) in the case of small rotational diffusion <span>(nu )</span> that the mixing estimates persist up to time scale <span>(nu ^{-1/2})</span> until the exponential decay at enhanced dissipation rate <span>(nu ^{1/2})</span> takes over. The interesting feature is that the usual velocity variable of kinetic models is replaced by an orientation variable on the sphere. The associated <i>orientation mixing</i> leads to limited algebraic decay for macroscopic quantities. For the proof, we start with a general pointwise decay result for Volterra equations that may be of independent interest. While, in the non-diffusive case, explicit formulas on the sphere allow to conclude the desired decay, much more work is required in the diffusive case: here we prove mixing estimates for the advection-diffusion equation on the sphere by combining an optimized hypocoercive approach with the vector field method. One main point in this context is to identify good commuting vector fields for the advection-diffusion operator on the sphere. Our results in this direction may be useful to other models in collective dynamics, where an orientation variable is involved.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"9 2","pages":""},"PeriodicalIF":2.8,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-023-00163-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50500692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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: 6

On the Transition of the Rayleigh-Taylor Instability in 2d Water Waves with Point Vortices 点涡二维水波Rayleigh-Taylor不稳定性的跃迁

IF 2.8 1区数学

Annals of Pde Pub Date : 2023-10-17 DOI: 10.1007/s40818-023-00157-6

Qingtang Su

引用次数: 1