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Communications on Pure and Applied Analysis最新文献

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Hydrodynamic limits of Manton's Schrödinger system 曼顿Schrödinger系统的水动力极限
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023066
Jeongho Kim, Bora Moon
{"title":"Hydrodynamic limits of Manton's Schrödinger system","authors":"Jeongho Kim, Bora Moon","doi":"10.3934/cpaa.2023066","DOIUrl":"https://doi.org/10.3934/cpaa.2023066","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221643","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
Polynomial stability of stochastic heat equations 随机热方程的多项式稳定性
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023092
G. Lv, Hongjun Gao, Jinlong Wei
{"title":"Polynomial stability of stochastic heat equations","authors":"G. Lv, Hongjun Gao, Jinlong Wei","doi":"10.3934/cpaa.2023092","DOIUrl":"https://doi.org/10.3934/cpaa.2023092","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221692","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: 1
On the Lyapunov exponent for some quasi-periodic cocycles with large parameter 一类大参数拟周期环的Lyapunov指数
3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023102
Bowen Ding, Jinhao Liang
{"title":"On the Lyapunov exponent for some quasi-periodic cocycles with large parameter","authors":"Bowen Ding, Jinhao Liang","doi":"10.3934/cpaa.2023102","DOIUrl":"https://doi.org/10.3934/cpaa.2023102","url":null,"abstract":"Lyapunov exponent plays an important role in the dynamics of quasi-periodic cocycles, and admits an asymptotic formula for Schrödinger cocycle with large parameter (see [12] for analytic case, and see [15] for finitely smooth case). In this paper, we establish similar asymptotic formulas of Lyapunov exponent for two classes of important quasi-periodic cocycles: Szegő cocycles and Schrödinger Mosaic cocycles.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135496200","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 synchronization of discrete-time Kuramoto model with frustration 带挫折的离散时间Kuramoto模型的同步问题
3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023109
Tingting Zhu
{"title":"On the synchronization of discrete-time Kuramoto model with frustration","authors":"Tingting Zhu","doi":"10.3934/cpaa.2023109","DOIUrl":"https://doi.org/10.3934/cpaa.2023109","url":null,"abstract":"In this paper, we study the emergent discrete-time dynamics of the Kuramoto model with frustration. For the discrete identical Kuramoto model with frustration, we present the exponential synchronization estimate for some admissible classes of initial configuration confined in a half circle. For the nonidentical oscillators, we exploit the second-order lifting of the original Kuramoto model with frustration and study the emergent behaviors of the corresponding discrete augmented model. More precisely, under a sufficient framework in terms of large coupling strength and small step size, we derive that the initial configuration distributed in a small set of a quarter circle will converge to frequency synchronization.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135700499","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
Onsager critical solutions of the forced Navier-Stokes equations 强迫Navier-Stokes方程的Onstager临界解
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2022-12-16 DOI: 10.3934/cpaa.2023071
Elia Brué, Maria Colombo, Gianluca Crippa, Camillo De Lellis, M. Sorella
{"title":"Onsager critical solutions of the forced Navier-Stokes equations","authors":"Elia Brué, Maria Colombo, Gianluca Crippa, Camillo De Lellis, M. Sorella","doi":"10.3934/cpaa.2023071","DOIUrl":"https://doi.org/10.3934/cpaa.2023071","url":null,"abstract":"We answer positively to [BDL22, Question 2.4] by building new examples of solutions to the forced 3d-Navier-Stokes equations with vanishing viscosity, which exhibit anomalous dissipation and which enjoy uniform bounds in the space $L_t^3 C_x^{1/3 - varepsilon}$, for any fixed $varepsilon>0$. Our construction combines ideas of [BDL22] and [CCS22].","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46111723","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: 9
On well-posedness for inhomogeneous Hartree equations in the critical case 临界情况下非齐次Hartree方程的适定性
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2022-12-14 DOI: 10.3934/cpaa.2023060
Seongyeon Kim
{"title":"On well-posedness for inhomogeneous Hartree equations in the critical case","authors":"Seongyeon Kim","doi":"10.3934/cpaa.2023060","DOIUrl":"https://doi.org/10.3934/cpaa.2023060","url":null,"abstract":"We study the well-posedness for the inhomogeneous Hartree equation $ipartial_t u + Delta u = lambda(I_alpha ast |cdot|^{-b}|u|^p)|x|^{-b}|u|^{p-2}u$ in $H^s$, $sge0$. Until recently, its well-posedness theory has been intensively studied, focusing on solving the problem for the critical index $p=1+frac{2-2b+alpha}{n-2s}$ with $0le s le 1$, but the case $1/2leq s leq 1$ is still an open problem. In this paper, we develop the well-posedness theory in this case, especially including the energy-critical case. To this end, we approach to the matter based on the Sobolev-Lorentz space which can lead us to perform a finer analysis for this equation. This is because it makes it possible to control the nonlinearity involving the singularity $|x|^{-b}$ as well as the Riesz potential $I_alpha$ more effectively.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48352822","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
Existence of weak solutions for some elliptic systems 一类椭圆型系统弱解的存在性
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2022-12-04 DOI: 10.2140/paa.2022.4.517
L. Boccardo, L. Orsina
{"title":"Existence of weak solutions for some elliptic systems","authors":"L. Boccardo, L. Orsina","doi":"10.2140/paa.2022.4.517","DOIUrl":"https://doi.org/10.2140/paa.2022.4.517","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79039601","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: 1
Existence of global strong solution for theNavier–Stokes–Korteweg system in one dimension for strongly degenerate viscositycoefficients 具有强退化粘滞系数的一维navier - stokes - korteweg系统全局强解的存在性
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2022-12-04 DOI: 10.2140/paa.2022.4.449
Cosmin Burtea, B. Haspot
{"title":"Existence of global strong solution for the\u0000Navier–Stokes–Korteweg system in one dimension for strongly degenerate viscosity\u0000coefficients","authors":"Cosmin Burtea, B. Haspot","doi":"10.2140/paa.2022.4.449","DOIUrl":"https://doi.org/10.2140/paa.2022.4.449","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76060094","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 attractors for a full von Karman beam transmission problem 全von—Karman光束传输问题的全局吸引子
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2022-11-07 DOI: 10.3934/cpaa.2023022
T. Fastovska
{"title":"Global attractors for a full von Karman beam transmission problem","authors":"T. Fastovska","doi":"10.3934/cpaa.2023022","DOIUrl":"https://doi.org/10.3934/cpaa.2023022","url":null,"abstract":"A nonlinear transmisson problem for an elastic full von Karman beam is considered here. We prove that the system possesses a compact global attractor.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49655490","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
Large solutions of elliptic semilinear equations non-degenerate near the boundary 椭圆型半线性方程在边界附近非退化的大解
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2022-10-31 DOI: 10.3934/cpaa.2023006
G. Díaz
{"title":"Large solutions of elliptic semilinear equations non-degenerate near the boundary","authors":"G. Díaz","doi":"10.3934/cpaa.2023006","DOIUrl":"https://doi.org/10.3934/cpaa.2023006","url":null,"abstract":"In this paper we study the so-called large solutions of elliptic semilinear equations with non null sources term, thus solutions blowing up on the boundary of the domain for which reason they are greater than any other solution whenever Weak Maximum Principle holds. The main topic about large solutions is uniqueness results and their behavior near the boundary. It is much less than being simple. The structure of the semilinear equations considered includes the well known Keller-Osserman integral and an assumption on the ellipticity of the leading part of the differential operator. In our study an uniform ellipticity near the boundary is required. We consider source terms in the PDE whose boundary explosion is consistent with the Keller-Osserman condition. Extra Keller-Osserman explosions on the source are also studied, showing in particular that in some cases the PDE only admits large solutions.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44136170","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: 1
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