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],...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.展开更多
基金supported by Natural Science Foundation of Fujian Province(JZ160406)partly supported by National Natural Science Foundation of China-NSAF(11271305 and 11531010)
文摘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.
