A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL L^P FRAMEWORK  

作　　者：Zhensheng GAO Yan LIANG Zhong TAN 高真圣;梁言;谭忠(School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China;School of Mathematical Sciences,Xiamen University,Xiamen 361005,China)

机构地区：[1]School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China [2]School of Mathematical Sciences,Xiamen University,Xiamen 361005,China

出　　处：《Acta Mathematica Scientia》2019年第6期1639-1660,共22页数学物理学报（B辑英文版）

基　　金：supported by Natural Science Foundation of Fujian Province(JZ160406);partly supported by National Natural Science Foundation of China-NSAF(11271305 and 11531010)

摘　　要：The purpose of this work is to investigate the initial value problem for a general isothermal model of capillary fluids derived by Dunn and Serrin [12], which can be used as a phase transition model. Motivated by [9], we aim at extending the work by DanchinDesjardins [11] to a critical framework which is not related to the energy space. For small perturbations of a stable equilibrium state in the sense of suitable L^p-type Besov norms,we establish the global existence. As a consequence, like for incompressible flows, one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true.The purpose of this work is to investigate the initial value problem for a general isothermal model of capillary fluids derived by Dunn and Serrin [12], which can be used as a phase transition model. Motivated by [9], we aim at extending the work by DanchinDesjardins [11] to a critical framework which is not related to the energy space. For small perturbations of a stable equilibrium state in the sense of suitable L^p-type Besov norms,we establish the global existence. As a consequence, like for incompressible flows, one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true.

关 键 词：Korteweg SYSTEM GLOBAL EXISTENCE L^p-type BESOV norms 

分 类 号：O17[理学—数学]