Pub Date : 2023-01-01DOI: 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}
Pub Date : 2023-01-01DOI: 10.4310/cms.2023.v21.n7.a9
Piotr B. Mucha, Wojciech S. Ożański
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 $epsilon>0$.
{"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}
Pub Date : 2023-01-01DOI: 10.4310/cms.2023.v21.n7.a4
Giada Cianfarani Carnevale, Corrado Lattanzio
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.
{"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}
Pub Date : 2023-01-01DOI: 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}
Pub Date : 2023-01-01DOI: 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}
Pub Date : 2023-01-01DOI: 10.4310/cms.2023.v21.n7.a10
Liang Guo, Fucai Li, Cheng Yu
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.
{"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}
Pub Date : 2023-01-01DOI: 10.4310/cms.2023.v21.n6.a1
Jinkai Li, Qiang Tao
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.
{"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}
Pub Date : 2023-01-01DOI: 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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：