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Stability of viscous contact wave for the full compressible Navier–Stokes–Korteweg equations with large perturbation 具有大扰动的全可压缩纳维-斯托克斯-科特韦格方程的粘性接触波的稳定性
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-08-01 DOI: 10.1088/1361-6544/ad61b4
Wenchao Dong
{"title":"Stability of viscous contact wave for the full compressible Navier–Stokes–Korteweg equations with large perturbation","authors":"Wenchao Dong","doi":"10.1088/1361-6544/ad61b4","DOIUrl":"https://doi.org/10.1088/1361-6544/ad61b4","url":null,"abstract":"This study focuses on the stability of the viscous contact wave for the one-dimensional full Navier–Stokes–Korteweg equations with density-temperature dependent transport coefficients and large perturbation. Our findings demonstrate a Nishida–Smoller type result, indicating that the solution remains stable under large perturbation as long as is sufficiently small. Notably, the smallness of the capillary coefficient is unnecessary. We then employ the initial layer analysis technique to investigate the asymptotic behaviour in the norm. We show that the capillary term has a smoothing effect, which implies that the strong solution is indeed a smooth one. Our results represent an improvement over those previously reported in Chen and Sheng (2019 Nonlinearity32 395–444). Furthermore, by applying the method in this study to the isothermal case, we can achieve a better outcome than Germain and LeFloch (2016 Commun. Pure Appl. Math.69 3–61).","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"21 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141882353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Fourier decay of equilibrium states for bunched attractors 成串吸引子平衡态的傅立叶衰减
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-08-01 DOI: 10.1088/1361-6544/ad6052
Gaétan Leclerc
{"title":"Fourier decay of equilibrium states for bunched attractors","authors":"Gaétan Leclerc","doi":"10.1088/1361-6544/ad6052","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6052","url":null,"abstract":"Let M be a closed manifold, and let be a Axiom A diffeomorphism. Suppose that f has an attractor Ω with codimension 1 stable lamination. Under a generic nonlinearity condition and a suitable bunching condition, we prove polynomial Fourier decay in the unstable direction for a large class of invariant measures on Ω. Our result applies in particular for the measure of maximal entropy. We construct in the appendix an explicit solenoid that satisfies the nonlinearity and bunching assumption.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"79 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141882352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 KP-mKP hierarchy via pseudo-differential operators with two derivations 通过具有两个导数的伪微分算子实现 KP-mKP 层次结构
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-31 DOI: 10.1088/1361-6544/ad64a4
Lumin Geng, Jianxun Hu, Chao-Zhong Wu
{"title":"A KP-mKP hierarchy via pseudo-differential operators with two derivations","authors":"Lumin Geng, Jianxun Hu, Chao-Zhong Wu","doi":"10.1088/1361-6544/ad64a4","DOIUrl":"https://doi.org/10.1088/1361-6544/ad64a4","url":null,"abstract":"By using pseudo-differential operators containing two derivations, we extend the Kadomtsev–Petviashvili (KP) hierarchy to a certain KP-mKP hierarchy. For the KP-mKP hierarchy, we derive its Bäcklund transformations, bilinear equations of Baker–Akhiezer functions and Hirota equations of tau functions. Moreover, we show that this hierarchy is equivalent to a subhierarchy of the dispersive Whitham hierarchy associated to the Riemann sphere with its infinity point and one movable point marked.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"52 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 stability of weak solutions of the Vlasov–Poisson system in localised Yudovich spaces 局部尤多维奇空间中弗拉索夫-泊松系统弱解的存在性和稳定性
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-25 DOI: 10.1088/1361-6544/ad5bb3
Gianluca Crippa, Marco Inversi, Chiara Saffirio and Giorgio Stefani
{"title":"Existence and stability of weak solutions of the Vlasov–Poisson system in localised Yudovich spaces","authors":"Gianluca Crippa, Marco Inversi, Chiara Saffirio and Giorgio Stefani","doi":"10.1088/1361-6544/ad5bb3","DOIUrl":"https://doi.org/10.1088/1361-6544/ad5bb3","url":null,"abstract":"We consider the Vlasov–Poisson system both in the repulsive (electrostatic potential) and in the attractive (gravitational potential) cases. Our first main theorem yields the analog for the Vlasov–Poisson system of Yudovich’s celebrated well-posedness theorem for the Euler equations: we prove the uniqueness and the quantitative stability of Lagrangian solutions whose associated spatial density is potentially unbounded but belongs to suitable uniformly-localised Yudovich spaces. This requirement imposes a condition of slow growth on the function uniformly in time. Previous works by Loeper, Miot and Holding–Miot have addressed the cases of bounded spatial density, i.e. , and spatial density such that for . Our approach is Lagrangian and relies on an explicit estimate of the modulus of continuity of the electric field and on a second-order Osgood lemma. It also allows for iterated-logarithmic perturbations of the linear growth condition. In our second main theorem, we complement the aforementioned result by constructing solutions whose spatial density sharply satisfies such iterated-logarithmic growth. Our approach relies on real-variable techniques and extends the strategy developed for the Euler equations by the first and fourth-named authors. It also allows for the treatment of more general equations that share the same structure as the Vlasov–Poisson system. Notably, the uniqueness result and the stability estimates hold for both the classical and the relativistic Vlasov–Poisson systems.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"26 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141771718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
New global exponential stability conditions for nonlinear delayed differential systems with three kinds of time-varying delays 具有三种时变延迟的非线性延迟微分系统的新全局指数稳定性条件
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-25 DOI: 10.1088/1361-6544/ad6126
Xian Zhang, Zhongjie Zhang, Yantao Wang and Xin Wang
{"title":"New global exponential stability conditions for nonlinear delayed differential systems with three kinds of time-varying delays","authors":"Xian Zhang, Zhongjie Zhang, Yantao Wang and Xin Wang","doi":"10.1088/1361-6544/ad6126","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6126","url":null,"abstract":"For a class of nonlinear differential systems with heterogeneous time-varying delays, including distributed, leakage and transmission time-varying delays, a novel global exponential stability (GES) analysis method was developed. Based on the GES definition, some sufficient conditions and rigorous convergence analysis of nonlinear delayed differential systems are presented directly, which ensure all states to be globally exponentially convergent. The proposed analysis method not only avoids the construction of the Lyapunov–Krasovskii functional, but also uses some simple integral reduction techniques to determine the global exponential convergence rate. Furthermore, the main advantages and low calculation complexity are demonstrated through a theoretical comparison. Finally, three numerical examples are provided to verify the effectiveness of the theoretical results.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"35 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141771720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Effective estimates of ergodic quantities illustrated on the Bolyai-Rényi map 波莱-雷尼图上说明的遍历量的有效估计值
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-24 DOI: 10.1088/1361-6544/ad6053
Mark Pollicott and Julia Slipantschuk
{"title":"Effective estimates of ergodic quantities illustrated on the Bolyai-Rényi map","authors":"Mark Pollicott and Julia Slipantschuk","doi":"10.1088/1361-6544/ad6053","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6053","url":null,"abstract":"We present a practical and effective method for rigorously estimating quantities associated to top eigenvalues of transfer operators to very high precision. The method combines explicit error bounds of the Lagrange-Chebyshev approximation with an established min-max method. We illustrate its applicability by significantly improving rigorous estimates on various ergodic quantities associated to the Bolyai–Rényi map.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"198 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141771721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Resonant solutions of the non-linear Schrödinger equation with periodic potential * 具有周期势能的非线性薛定谔方程的共振解 *
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-23 DOI: 10.1088/1361-6544/ad6127
Arein Duaibes and Yulia Karpeshina
{"title":"Resonant solutions of the non-linear Schrödinger equation with periodic potential *","authors":"Arein Duaibes and Yulia Karpeshina","doi":"10.1088/1361-6544/ad6127","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6127","url":null,"abstract":"The goal is construction of stationary solutions close to non-trivial combinations of two plane waves at high energies for a periodic non-linear Schrödinger Equation in dimension two. The corresponding isoenergetic surface is described for any sufficiently large energy k2. It is shown that the isoenergetic surface corresponding to k2 is essentially different from that for the zero potential even for small potentials. We use a combination of the perturbative results obtained earlier for the linear case and a method of successive approximation.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"21 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141771722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Wm -algebras and fractional powers of difference operators Wm 矩阵和差分算子的分数幂
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-22 DOI: 10.1088/1361-6544/ad5fd8
Gloria Marí Beffa
{"title":"Wm -algebras and fractional powers of difference operators","authors":"Gloria Marí Beffa","doi":"10.1088/1361-6544/ad5fd8","DOIUrl":"https://doi.org/10.1088/1361-6544/ad5fd8","url":null,"abstract":"In this paper we define a Poisson pencil associated to a lattice Wm-algebras defined in a recent paper by Izosimov and Marí Beffa (2023 Int. Math. Res. Not.2023 17021–59). We then prove that this Poisson pencil is equal to the one defined in 2013 by Marí Beffa and Wang (2013 Nonlinearity26 2515) and the author using a type of discrete Drinfel’d–Sokolov reduction. We then show that, much as in the continuous case, a family of Hamiltonians defined by fractional powers of difference operators commute with respect to both structures, defining the kernel of one of them and creating an integrable hierarchy in the Liouville sense.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"28 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141754117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Necessary and sufficient conditions for Kolmogorov’s flux laws on T2 and T3 T2 和 T3 上的柯尔莫哥洛夫通量定律的必要条件和充分条件
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-22 DOI: 10.1088/1361-6544/ad5924
Ethan Dudley
{"title":"Necessary and sufficient conditions for Kolmogorov’s flux laws on T2 and T3","authors":"Ethan Dudley","doi":"10.1088/1361-6544/ad5924","DOIUrl":"https://doi.org/10.1088/1361-6544/ad5924","url":null,"abstract":"Necessary and sufficient conditions for the third order Kolmogorov universal scaling flux laws are derived for the stochastically forced incompressible Navier Stokes equations on the torus in 2D and 3D. This paper rigorously generalises the result of (Bedrossian 2019 Commun. Math. Phys.367 1045–75) to functions which are heavy-tailed in Fourier space or have local finite time singularities in the inviscid limit. In other words, we have rigorously derived the existence of the well known physical relationships, the direct and inverse cascades. Furthermore we show that the rate of the direct cascade is proportional to the amount of energy ‘escaping to infinity’ in spectral space as well as a measure of the total singularities within the solution. Similarly, an inverse cascade is proportional to the amount of energy that moves towards the k = 0 Fourier mode in the invisicid limit.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"75 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141754115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Accelerated relaxation enhancing flows cause total dissipation 加速弛豫增强流导致完全耗散
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-21 DOI: 10.1088/1361-6544/ad6054
Keefer Rowan
{"title":"Accelerated relaxation enhancing flows cause total dissipation","authors":"Keefer Rowan","doi":"10.1088/1361-6544/ad6054","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6054","url":null,"abstract":"We show that by ‘accelerating’ relaxation enhancing flows, one can construct a flow that is smooth on but highly singular at t = 1 so that for any positive diffusivity, the advection–diffusion equation associated to the accelerated flow totally dissipates solutions, taking arbitrary initial data to the constant function at t = 1.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"105 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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