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Journal of Hyperbolic Differential Equations最新文献

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Smoothing and growth bound of periodic generalized Korteweg–De Vries equation 周期广义Korteweg-De Vries方程的平滑和生长界
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2020-01-24 DOI: 10.1142/s0219891621500260
Seungly Oh, A. Stefanov
{"title":"Smoothing and growth bound of periodic generalized Korteweg–De Vries equation","authors":"Seungly Oh, A. Stefanov","doi":"10.1142/s0219891621500260","DOIUrl":"https://doi.org/10.1142/s0219891621500260","url":null,"abstract":"For generalized Korteweg–De Vries (KdV) models with polynomial nonlinearity, we establish a local smoothing property in [Formula: see text] for [Formula: see text]. Such smoothing effect persists globally, provided that the [Formula: see text] norm does not blow up in finite time. More specifically, we show that a translate of the nonlinear part of the solution gains [Formula: see text] derivatives for [Formula: see text]. Following a new simple method, which is of independent interest, we establish that, for [Formula: see text], [Formula: see text] norm of a solution grows at most by [Formula: see text] if [Formula: see text] norm is a priori controlled.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45606017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 6
WKB expansions for weakly well-posed hyperbolic boundary value problems in a strip: Time depending loss of derivatives 带上弱适定双曲边值问题的WKB展开式:导数的随时间损失
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-12-03 DOI: 10.1142/s0219891621500181
Antoine Benoit
{"title":"WKB expansions for weakly well-posed hyperbolic boundary value problems in a strip: Time depending loss of derivatives","authors":"Antoine Benoit","doi":"10.1142/s0219891621500181","DOIUrl":"https://doi.org/10.1142/s0219891621500181","url":null,"abstract":"We are interested in geometric optics expansions for linear hyperbolic systems of equations defined in the strip [Formula: see text]. More precisely the aim of this paper is to describe the influence of the boundary conditions on the behavior of the solution. This question has already been addressed in [A. Benoit, Wkb expansions for hyperbolic boundary value problems in a strip: Selfinteraction meets strong well-posedness, J. Inst. Math. Jussieu 19(5) (2020) 1629–1675] for stable boundary conditions. Here we do not require that the boundary conditions lead to strongly well-posed problems but only to weakly well-posed problems (that is loss(es) of derivatives are possible). The question is thus to determine what can be the minimal loss of derivatives in the energy estimate of the solution. The main result of this paper is to show, thanks to geometric optics expansions, that if the strip problem admits a boundary in the so-called [Formula: see text]-class of [S. Benzoni-Gavage, F. Rousset, D. Serre and K. Zumbrun, Generic types and transitions in hyperbolic initial-boundary-value problems, Proc. Roy. Soc. Edinburgh Sect. A 132(5) (2002) 1073–1104] then the loss of derivatives shall be at least increasing with the time of resolution. More precisely this loss is bounded by below by a step function increasing with respect to time which depends on the minimal time needed to perform a full regeneration of the wave packet.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45993363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Lp time asymptotic decay for general hyperbolic–parabolic balance laws with applications 一般双曲-抛物平衡律的Lp时间渐近衰减及其应用
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-12-01 DOI: 10.1142/s021989161950022x
Yanni Zeng
{"title":"Lp time asymptotic decay for general hyperbolic–parabolic balance laws with applications","authors":"Yanni Zeng","doi":"10.1142/s021989161950022x","DOIUrl":"https://doi.org/10.1142/s021989161950022x","url":null,"abstract":"We study the time asymptotic decay of solutions for a general system of hyperbolic–parabolic balance laws in one space dimension. The system has a physical viscosity matrix and a lower-order term f...","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":"16 1","pages":"663-700"},"PeriodicalIF":0.7,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/s021989161950022x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45161967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Strong solutions to the density-dependent incompressible Cahn–Hilliard–Navier–Stokes system 密度相关不可压缩Cahn-Hilliard-Navier-Stokes系统的强解
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-12-01 DOI: 10.1142/s0219891619500231
Xiaopeng Zhao
{"title":"Strong solutions to the density-dependent incompressible Cahn–Hilliard–Navier–Stokes system","authors":"Xiaopeng Zhao","doi":"10.1142/s0219891619500231","DOIUrl":"https://doi.org/10.1142/s0219891619500231","url":null,"abstract":"We study the density-dependent incompressible Cahn–Hilliard–Navier–Stokes system, which describes a two-phase flow of two incompressible fluids with different densities. We establish the local exis...","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":"16 1","pages":"701-742"},"PeriodicalIF":0.7,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/s0219891619500231","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47365128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 6
Well-posedness and blow-up criterion for the Chaplygin gas equations in ℝN 方程的适定性和爆破判据
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-12-01 DOI: 10.1142/s0219891619500218
Zhen Wang, Xing-Ping Wu
{"title":"Well-posedness and blow-up criterion for the Chaplygin gas equations in ℝN","authors":"Zhen Wang, Xing-Ping Wu","doi":"10.1142/s0219891619500218","DOIUrl":"https://doi.org/10.1142/s0219891619500218","url":null,"abstract":"We establish a well-posedness theory and a blow-up criterion for the Chaplygin gas equations in ℝN for any dimension N ≥ 1. First, given ω = 1 ρ, ℋ↪𝒞0,1, we prove the well-posedness property for so...","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":"16 1","pages":"639-661"},"PeriodicalIF":0.7,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/s0219891619500218","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42755872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Global large solutions to planar magnetohydrodynamics equations with temperature-dependent coefficients 具有温度相关系数的平面磁流体动力学方程的全局大解
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-10-21 DOI: 10.1142/s0219891619500164
Yachun Li, Zhaoyang Shang
{"title":"Global large solutions to planar magnetohydrodynamics equations with temperature-dependent coefficients","authors":"Yachun Li, Zhaoyang Shang","doi":"10.1142/s0219891619500164","DOIUrl":"https://doi.org/10.1142/s0219891619500164","url":null,"abstract":"We consider the planar compressible magnetohydrodynamics (MHD) system for a viscous and heat-conducting ideal polytropic gas, when the viscosity, magnetic diffusion and heat conductivity depend on the specific volume [Formula: see text] and the temperature [Formula: see text]. For technical reasons, the viscosity coefficients, magnetic diffusion and heat conductivity are assumed to be proportional to [Formula: see text] where [Formula: see text] is a non-degenerate and smooth function satisfying some natural conditions. We prove the existence and uniqueness of the global-in-time classical solution to the initial-boundary value problem when general large initial data are prescribed and the exponent [Formula: see text] is sufficiently small. A similar result is also established for planar Hall-MHD equations.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/s0219891619500164","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47857152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 6
Local well-posedness of the two-dimensional Dirac–Klein–Gordon equations in Fourier–Lebesgue spaces 傅立叶-勒贝格空间中二维Dirac-Klein-Gordon方程的局部适定性
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-10-09 DOI: 10.1142/S0219891620500241
H. Pecher
{"title":"Local well-posedness of the two-dimensional Dirac–Klein–Gordon equations in Fourier–Lebesgue spaces","authors":"H. Pecher","doi":"10.1142/S0219891620500241","DOIUrl":"https://doi.org/10.1142/S0219891620500241","url":null,"abstract":"The local well-posedness problem is considered for the Dirac–Klein–Gordon system in two space dimensions for data in Fourier–Lebesgue spaces [Formula: see text], where [Formula: see text] and [Formula: see text] and [Formula: see text] denote dual exponents. We lower the regularity assumptions on the data with respect to scaling improving the results of d’Ancona et al. in the classical case [Formula: see text]. Crucial is the fact that the nonlinearities fulfill a null condition as detected by these authors.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46045807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Growth-in-time of higher Sobolev norms of solutions to the 1D Dirac–Klein–Gordon system 一维Dirac-Klein-Gordon系统解的高Sobolev范数随时间的增长
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-08-21 DOI: 10.1142/S0219891619500127
Achenef Tesfahun
{"title":"Growth-in-time of higher Sobolev norms of solutions to the 1D Dirac–Klein–Gordon system","authors":"Achenef Tesfahun","doi":"10.1142/S0219891619500127","DOIUrl":"https://doi.org/10.1142/S0219891619500127","url":null,"abstract":"We study the growth-in-time of higher order Sobolev norms of solutions to the Dirac–Klein–Gordon (DKG) equations in one space dimension. We show that these norms grow at most polynomially-in-time. The main ingredients in the proof are the upside-down [Formula: see text]-method which was introduced by Colliander, Keel, Staffilani, Takaoka and Tao, and bilinear null-form estimates.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219891619500127","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41906778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Classical solutions to a dissipative hyperbolic geometry flow in two space variables 两个空间变量中耗散双曲几何流的经典解
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-08-21 DOI: 10.1142/S0219891619500085
D. Kong, Qi Liu, Changming Song
{"title":"Classical solutions to a dissipative hyperbolic geometry flow in two space variables","authors":"D. Kong, Qi Liu, Changming Song","doi":"10.1142/S0219891619500085","DOIUrl":"https://doi.org/10.1142/S0219891619500085","url":null,"abstract":"We investigate a dissipative hyperbolic geometry flow in two space variables for which a new nonlinear wave equation is derived. Based on an energy method, the global existence of solutions to the dissipative hyperbolic geometry flow is established. Furthermore, the scalar curvature of the metric remains uniformly bounded. Moreover, under suitable assumptions, we establish the global existence of classical solutions to the Cauchy problem, and we show that the solution and its derivative decay to zero as the time tends to infinity. In addition, the scalar curvature of the solution metric converges to the one of the flat metric at an algebraic rate.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219891619500085","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45788218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A priori estimates in Sobolev spaces for a class of hyperbolic operators in presence of transition 一类存在转移的双曲算子在Sobolev空间中的先验估计
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-08-21 DOI: 10.1142/S0219891619500097
A. Barbagallo, V. Esposito
{"title":"A priori estimates in Sobolev spaces for a class of hyperbolic operators in presence of transition","authors":"A. Barbagallo, V. Esposito","doi":"10.1142/S0219891619500097","DOIUrl":"https://doi.org/10.1142/S0219891619500097","url":null,"abstract":"We establish several a priori estimates of local or global nature in Sobolev spaces with general exponent [Formula: see text] for a class of second-order hyperbolic operators with double characteristics in presence of a transition in a domain of the Euclidian space [Formula: see text].","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219891619500097","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48089808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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