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Stability of planar rarefaction wave for viscous vasculogenesis model 粘性血管生成模型平面稀疏波的稳定性
4区 数学
Communications in Mathematical Sciences Pub Date : 2023-01-01 DOI: 10.4310/cms.2023.v21.n8.a9
Qingqing Liu, Yuxiu Tian
{"title":"Stability of planar rarefaction wave for viscous vasculogenesis model","authors":"Qingqing Liu, Yuxiu Tian","doi":"10.4310/cms.2023.v21.n8.a9","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n8.a9","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135712010","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
Flocking behavior of the Cucker–Smale model under a general digraph on the infinite cylinder 无限圆柱上一般有向图下cucker - small模型的群集行为
4区 数学
Communications in Mathematical Sciences Pub Date : 2023-01-01 DOI: 10.4310/cms.2023.v21.n8.a11
Xiaoyu Li, Lining Ru
{"title":"Flocking behavior of the Cucker–Smale model under a general digraph on the infinite cylinder","authors":"Xiaoyu Li, Lining Ru","doi":"10.4310/cms.2023.v21.n8.a11","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n8.a11","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135712026","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
Global-in-time stability of ground states of a pressureless hydrodynamic model of collective behaviour 集体行为无压水动力模型基态的全局实时稳定性
4区 数学
Communications in Mathematical Sciences Pub Date : 2023-01-01 DOI: 10.4310/cms.2023.v21.n7.a9
Piotr B. Mucha, Wojciech S. Ożański
{"title":"Global-in-time stability of ground states of a pressureless hydrodynamic model of collective behaviour","authors":"Piotr B. Mucha, Wojciech S. Ożański","doi":"10.4310/cms.2023.v21.n7.a9","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n7.a9","url":null,"abstract":"We consider a pressureless hydrodynamic model of collective behaviour, which is concerned with a density function $rho$ and a velocity field $v$ on the torus, and is described by the continuity equation for $rho$, $partial_t rho + mathrm{div} (vrho )=0$, and a compressible hydrodynamic equation for $v$, $rho v_t + rho vcdot nabla v - Delta v = -rho nabla K rho$ with a forcing modelling collective behaviour related to the density $rho$, where $K$ stands for the interaction potential, defined as the solution to the Poisson equation on $mathbb{T}^d$. We show global-in-time stability of the ground state $(rho , v)=(1,0)$ if the perturbation $(rho_0-1 ,v_0)$ satisfies $| v_0 |_{B^{d/p-1}_{p,1}(mathbb{T}^d )} + | rho_0-1 |_{B^{d/p}_{p,1}(mathbb{T}^d )} leq epsilon$ for sufficiently small $epsilon>0$.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136052514","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
High friction limits of Euler–Navier–Stokes–Korteweg equations for multicomponent models 多分量模型的Euler-Navier-Stokes-Korteweg方程的高摩擦极限
4区 数学
Communications in Mathematical Sciences Pub Date : 2023-01-01 DOI: 10.4310/cms.2023.v21.n7.a4
Giada Cianfarani Carnevale, Corrado Lattanzio
{"title":"High friction limits of Euler–Navier–Stokes–Korteweg equations for multicomponent models","authors":"Giada Cianfarani Carnevale, Corrado Lattanzio","doi":"10.4310/cms.2023.v21.n7.a4","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n7.a4","url":null,"abstract":"In this paper we analyze the high friction regime for the Navier Stokes Korteweg equations for multicomponent systems. According to the shape of the mixing and friction terms, we shall perform two limits: the high friction limit toward an equilibrium system for the limit densities and the barycentric velocity, and, after an appropriate time scaling, the diffusive relaxation toward parabolic, gradient flow equations for the limit densities. The rigorous justification of these limits is done by means of relative entropy techniques in the framework of weak, finite energy solutions of the relaxation models, rewritten in the enlarged formulation in terms of the drift velocity, toward smooth solutions of the corresponding equilibrium dynamics. Finally, since our estimates are uniform for small viscosity, the results are also valid for the Euler Korteweg multicomponent models, and the corresponding estimates can be obtained by sending the viscosity to zero.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136054195","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
Global-in-time classical solutions to two-dimensional axisymmetric Euler system with swirl 含旋流的二维轴对称欧拉系统的全局时域经典解
IF 1 4区 数学
Communications in Mathematical Sciences Pub Date : 2023-01-01 DOI: 10.4310/cms.2023.v21.n3.a9
G. Lai, M. Zhu
{"title":"Global-in-time classical solutions to two-dimensional axisymmetric Euler system with swirl","authors":"G. Lai, M. Zhu","doi":"10.4310/cms.2023.v21.n3.a9","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n3.a9","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"11 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70421952","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
Semiconductor full quantum hydrodynamic model with non-flat doping profile: I) Stability of steady state 非平坦掺杂型半导体全量子流体力学模型:1)稳态稳定性
IF 1 4区 数学
Communications in Mathematical Sciences Pub Date : 2023-01-01 DOI: 10.4310/cms.2023.v21.n5.a2
Haifeng Hu, Kaijun Zhang
{"title":"Semiconductor full quantum hydrodynamic model with non-flat doping profile: I) Stability of steady state","authors":"Haifeng Hu, Kaijun Zhang","doi":"10.4310/cms.2023.v21.n5.a2","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n5.a2","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70422155","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
Existence and uniqueness for “good” Boussinesq equations with quasi-periodic initial data 具有拟周期初始数据的“好”Boussinesq方程的存在唯一性
IF 1 4区 数学
Communications in Mathematical Sciences Pub Date : 2023-01-01 DOI: 10.4310/cms.2023.v21.n5.a3
Yixian Gao, Yong Li, Chang Su
{"title":"Existence and uniqueness for “good” Boussinesq equations with quasi-periodic initial data","authors":"Yixian Gao, Yong Li, Chang Su","doi":"10.4310/cms.2023.v21.n5.a3","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n5.a3","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70422190","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
Dissipative solutions to the compressible isentropic Navier–Stokes equations 可压缩等熵Navier-Stokes方程的耗散解
4区 数学
Communications in Mathematical Sciences Pub Date : 2023-01-01 DOI: 10.4310/cms.2023.v21.n7.a10
Liang Guo, Fucai Li, Cheng Yu
{"title":"Dissipative solutions to the compressible isentropic Navier–Stokes equations","authors":"Liang Guo, Fucai Li, Cheng Yu","doi":"10.4310/cms.2023.v21.n7.a10","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n7.a10","url":null,"abstract":"The existence of dissipative solutions to the compressible isentropic Navier-Stokes equations was established in this paper. This notion was inspired by the concept of dissipative solutions to the incompressible Euler equations of Lions (cite{Lions-1996}, Section 4.4). Our method is to recover such solutions by passing to the limits from approximated solutions, thanks to compactness argument.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135783917","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
Global small solutions to heat conductive compressible nematic liquid crystal system: smallness on a scaling invariant quantity 导热可压缩向列液晶系统的全局小解:尺度不变量上的小
4区 数学
Communications in Mathematical Sciences Pub Date : 2023-01-01 DOI: 10.4310/cms.2023.v21.n6.a1
Jinkai Li, Qiang Tao
{"title":"Global small solutions to heat conductive compressible nematic liquid crystal system: smallness on a scaling invariant quantity","authors":"Jinkai Li, Qiang Tao","doi":"10.4310/cms.2023.v21.n6.a1","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n6.a1","url":null,"abstract":"In this paper, we consider the Cauchy problem to the three dimensional heat conducting compressible nematic liquid crystal system in the presence of vacuum and with vacuum far fields. Global well-posedness of strong solutions is established under the condition that the scaling invariant quantity $ (|rho_0|_infty+1)big[|rho_0|_3+(|rho_0|_infty+1)^2(|sqrt{rho_0}u_0|_2^2+ |nabla d_0|_2^2)big] big[|nabla u_0|_2^2+(|rho_0|_infty+1)(|sqrt{rho_0}E_0|_2^2 + |nabla^2 d_0|_2^2)big]$ is sufficiently small with the smallness depending only on the parameters appeared in the system.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135649892","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
Low-Mach type approximation of the Navier–Stokes system with temperature and salinity for free surface flows 自由表面流动的带温度和盐度的Navier-Stokes系统的低马赫近似
IF 1 4区 数学
Communications in Mathematical Sciences Pub Date : 2023-01-01 DOI: 10.4310/cms.2023.v21.n1.a7
Léa Boittin, M. Bristeau, F. Bouchut, A. Mangeney, Jacques Sainte-Marie, Fabien Souillé
{"title":"Low-Mach type approximation of the Navier–Stokes system with temperature and salinity for free surface flows","authors":"Léa Boittin, M. Bristeau, F. Bouchut, A. Mangeney, Jacques Sainte-Marie, Fabien Souillé","doi":"10.4310/cms.2023.v21.n1.a7","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n1.a7","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70421471","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
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