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Journal of Hyperbolic Differential Equations最新文献

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Small data global regularity and scattering for 3D Ericksen–Leslie compressible hyperbolic liquid crystal model 三维Ericksen–Leslie可压缩双曲型液晶模型的小数据全局正则性和散射
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-05-13 DOI: 10.1142/S0219891622500199
Jiaxi Huang, Ning Jiang, Yi-Long Luo, Lifeng Zhao
{"title":"Small data global regularity and scattering for 3D Ericksen–Leslie compressible hyperbolic liquid crystal model","authors":"Jiaxi Huang, Ning Jiang, Yi-Long Luo, Lifeng Zhao","doi":"10.1142/S0219891622500199","DOIUrl":"https://doi.org/10.1142/S0219891622500199","url":null,"abstract":"We study the Ericksen–Leslie hyperbolic system for compressible liquid crystal model in three spatial dimensions. Global regularity and scattering for small and smooth initial data near equilibrium are proved for the case that the system is a nonlinear coupling of compressible Navier–Stokes equations with wave map to [Formula: see text]. The main strategy relies on an interplay between the control of high order energies and decay estimates, which is based on the idea inspired by the method of space-time resonances. Unlike the incompressible model, the different behaviors of the decay properties of the density and velocity field for compressible fluids at different frequencies play a key role, which is a particular feature of compressible model.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49139461","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: 5
Asymptotic profiles for damped plate equations with rotational inertia terms 含转动惯量项的阻尼板方程的渐近轮廓
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-05-10 DOI: 10.1142/s0219891620500162
Tomonori Fukushima, R. Ikehata, Hironori Michihisa
{"title":"Asymptotic profiles for damped plate equations with rotational inertia terms","authors":"Tomonori Fukushima, R. Ikehata, Hironori Michihisa","doi":"10.1142/s0219891620500162","DOIUrl":"https://doi.org/10.1142/s0219891620500162","url":null,"abstract":"We consider the Cauchy problem for plate equations with rotational inertia and frictional damping terms. We derive asymptotic profiles of the solution in [Formula: see text]-sense as [Formula: see text] in the case when the initial data have high and low regularity, respectively. Especially, in the low regularity case of the initial data one encounters the regularity-loss structure of the solutions, and the analysis is more delicate. We employ the so-called Fourier splitting method combined with the explicit formula of the solution (high-frequency estimates) and the method due to [R. Ikehata, Asymptotic profiles for wave equations with strong damping, J. Differential Equations 257 (2014) 2159–2177.] (low-frequency estimates). In this paper, we will introduce a new threshold [Formula: see text] on the regularity of the initial data that divides the property of the corresponding solution to our problem into two parts: one is wave-like, and the other is parabolic-like.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42593626","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: 4
Well-posedness theory for stochastically forced conservation laws on Riemannian manifolds 黎曼流形上随机强迫守恒定律的适定性理论
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-04-07 DOI: 10.1142/s0219891619500188
Luca Galimberti, K. Karlsen
{"title":"Well-posedness theory for stochastically forced conservation laws on Riemannian manifolds","authors":"Luca Galimberti, K. Karlsen","doi":"10.1142/s0219891619500188","DOIUrl":"https://doi.org/10.1142/s0219891619500188","url":null,"abstract":"We investigate a class of scalar conservation laws on manifolds driven by multiplicative Gaussian (Itô) noise. The Cauchy problem defined on a Riemanian manifold is shown to be well-posed. We prove existence of generalized kinetic solutions using the vanishing viscosity method. A rigidity result àla Perthame is derived, which implies that generalized solutions are kinetic solutions and that kinetic solutions are uniquely determined by their initial data ([Formula: see text] contraction principle). Deprived of noise, the equations we consider coincide with those analyzed by Ben-Artzi and LeFloch [Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds, Ann. Inst. H. Poincaré Anal. Non Linéaire 24(6) (2007) 989–1008], who worked with Kružkov–DiPerna solutions. In the Euclidian case, the stochastic equations agree with those examined by Debussche and Vovelle [Scalar conservation laws with stochastic forcing, J. Funct. Anal. 259(4) (2010) 1014–1042].","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/s0219891619500188","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49415532","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: 5
The Suliciu approximate Riemann solver is not invariant domain preserving Suliciu近似黎曼解不是不变保域的
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-03-01 DOI: 10.1142/S0219891619500036
J. Guermond, C. Klingenberg, B. Popov, I. Tomas
{"title":"The Suliciu approximate Riemann solver is not invariant domain preserving","authors":"J. Guermond, C. Klingenberg, B. Popov, I. Tomas","doi":"10.1142/S0219891619500036","DOIUrl":"https://doi.org/10.1142/S0219891619500036","url":null,"abstract":"We show that the first-order finite volume technique based on the Suliciu approximate Riemann solver, while being positive, violates the invariant domain properties of the [Formula: see text]-system.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219891619500036","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46024242","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
Resonance in rarefaction and shock curves: Local analysis and numerics of the continuation method 稀疏和激波曲线中的共振:延拓法的局部分析和数值
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-02-11 DOI: 10.1142/S0219891620500198
A. C. Alvarez, G. Goedert, D. Marchesin
{"title":"Resonance in rarefaction and shock curves: Local analysis and numerics of the continuation method","authors":"A. C. Alvarez, G. Goedert, D. Marchesin","doi":"10.1142/S0219891620500198","DOIUrl":"https://doi.org/10.1142/S0219891620500198","url":null,"abstract":"We describe certain crucial steps in the development of an algorithm for finding the Riemann solution to systems of conservation laws. We relax the classical hypotheses of strict hyperbolicity and genuine nonlinearity due to Lax. First, we present a procedure for continuing wave curves beyond points where characteristic speeds coincide, i.e. at wave curve points of maximal co-dimensionality. This procedure requires strict hyperbolicity on both sides of the coincidence locus. Loss of strict hyperbolicity is regularized by means of a Generalized Jordan Chain, which serves to construct a four-fold sub-manifold structure on which wave curves can be continued. Second, we analyze the loss of genuine nonlinearity. We prove a new result: the existence of composite wave curves when the composite wave traverses either the inflection locus or an anomalous part of the non-local composite wave curve. In this sense, we find conditions under which the composite field is well defined and its singularities can be removed, allowing use of our continuation method. Finally, we present numerical examples for a non-strictly hyperbolic system of conservation laws.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42896852","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: 4
Boundedness of planar jump discontinuities for homogeneous hyperbolic systems 齐次双曲型系统平面跳跃间断的有界性
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2019-01-13 DOI: 10.1142/s0219891621500168
J. Rauch
{"title":"Boundedness of planar jump discontinuities for homogeneous hyperbolic systems","authors":"J. Rauch","doi":"10.1142/s0219891621500168","DOIUrl":"https://doi.org/10.1142/s0219891621500168","url":null,"abstract":"Suppose that [Formula: see text] is a homogeneous constant coefficient strongly hyperbolic partial differential operator on [Formula: see text] and that [Formula: see text] is a characteristic hyperplane. Suppose that in a conic neighborhood of the conormal variety of [Formula: see text], the characteristic variety of [Formula: see text] is the graph of a real analytic function [Formula: see text] with [Formula: see text] identically equal to zero or the maximal possible value [Formula: see text]. Suppose that the source function [Formula: see text] is compactly supported in [Formula: see text] and piecewise smooth with singularities only on [Formula: see text]. Then the solution of [Formula: see text] with [Formula: see text] for [Formula: see text] is uniformly bounded on [Formula: see text]. Typically when [Formula: see text] on the conormal variety, the sup norm of the jump in the gradient of [Formula: see text] across [Formula: see text] grows linearly with [Formula: see text].","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43962878","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
Three-phase fluid displacements in a porous medium 多孔介质中的三相流体位移
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2018-12-01 DOI: 10.1142/S0219891618500236
P. Andrade, A. J. Souza, F. Furtado, D. Marchesin
{"title":"Three-phase fluid displacements in a porous medium","authors":"P. Andrade, A. J. Souza, F. Furtado, D. Marchesin","doi":"10.1142/S0219891618500236","DOIUrl":"https://doi.org/10.1142/S0219891618500236","url":null,"abstract":"Oil in a reservoir is usually found together with water and gas. Often a mixture of water and gas is used to displace such oil. In this work, we present the Riemann solution for such three-phase flow problem. This solution encodes the dependence of recovery on the injected proportion, the proportion initially present, and the viscosity of the several fluids. We use the wave curve method to determine the Riemann solution for initial and injection data in the above-mentioned class. We verify the [Formula: see text]-stability of the Riemann solution with variation of data. We do not establish uniqueness of the Riemann solution, but we believe that it is valid.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219891618500236","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49254537","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
Breaking symmetry in focusing nonlinear Klein-Gordon equations with potential 带势聚焦非线性Klein-Gordon方程的破缺对称性
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2018-12-01 DOI: 10.1142/S0219891618500248
V. Georgiev, S. Lucente
{"title":"Breaking symmetry in focusing nonlinear Klein-Gordon equations with potential","authors":"V. Georgiev, S. Lucente","doi":"10.1142/S0219891618500248","DOIUrl":"https://doi.org/10.1142/S0219891618500248","url":null,"abstract":"We study the dynamics for the focusing nonlinear Klein–Gordon equation, [Formula: see text] with positive radial potential [Formula: see text] and initial data in the energy space. Under suitable assumption on the potential, we establish the existence and uniqueness of the ground state solution. This enables us to define a threshold size for the initial data that separates global existence and blow-up. An appropriate Gagliardo–Nirenberg inequality gives a critical exponent depending on [Formula: see text]. For subcritical exponent and subcritical energy global existence vs blow-up conditions are determined by a comparison between the nonlinear term of the energy solution and the nonlinear term of the ground state energy. For subcritical exponents and critical energy some solutions blow-up, other solutions exist for all time due to the decomposition of the energy space of the initial data into two complementary domains.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219891618500248","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42515048","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
Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations 等熵可压缩二维欧拉方程能量守恒解的非唯一性
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2018-12-01 DOI: 10.1142/S0219891618500224
C. Klingenberg, Simon Markfelder
{"title":"Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations","authors":"C. Klingenberg, Simon Markfelder","doi":"10.1142/S0219891618500224","DOIUrl":"https://doi.org/10.1142/S0219891618500224","url":null,"abstract":"We consider the 2-d isentropic compressible Euler equations. It was shown in [E. Chiodaroli, C. De Lellis and O. Kreml, Global ill-posedness of the isentropic system of gas dynamics, Comm. Pure Appl. Math. 68(7) (2015) 1157–1190] that there exist Riemann initial data as well as Lipschitz initial data for which there exist infinitely many weak solutions that fulfill an energy inequality. In this paper, we will prove that there is Riemann initial data for which there exist infinitely many weak solutions that conserve energy, i.e. they fulfill an energy equality. As in the aforementioned paper, we will also show that there even exist Lipschitz initial data with the same property.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219891618500224","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63943752","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: 5
Regularity of weak solutions for the relativistic Vlasov–Maxwell system 相对论性Vlasov–Maxwell系统弱解的正则性
IF 0.7 4区 数学
Journal of Hyperbolic Differential Equations Pub Date : 2018-12-01 DOI: 10.1142/S0219891618500212
N. Besse, Philippe Bechouche
{"title":"Regularity of weak solutions for the relativistic Vlasov–Maxwell system","authors":"N. Besse, Philippe Bechouche","doi":"10.1142/S0219891618500212","DOIUrl":"https://doi.org/10.1142/S0219891618500212","url":null,"abstract":"We investigate the regularity of weak solutions of the relativistic Vlasov–Maxwell system by using Fourier analysis and the smoothing effect of low velocity particles. This smoothing effect has been used by several authors (see Glassey and Strauss 1986; Klainerman and Staffilani, 2002) for proving existence and uniqueness of [Formula: see text]-regular solutions of the Vlasov–Maxwell system. This smoothing mechanism has also been used to study the regularity of solutions for a kinetic transport equation coupled with a wave equation (see Bouchut, Golse and Pallard 2004). Under the same assumptions as in the paper “Nonresonant smoothing for coupled wave[Formula: see text]+[Formula: see text]transport equations and the Vlasov–Maxwell system”, Rev. Mat. Iberoamericana 20 (2004) 865–892, by Bouchut, Golse and Pallard, we prove a slightly better regularity for the electromagnetic field than the one showed in the latter paper. Namely, we prove that the electromagnetic field belongs to [Formula: see text], with [Formula: see text].","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1142/S0219891618500212","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46977299","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: 8
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