摘要
In this paper, we investigate non-isothermal one-dimensional model of capillary compressible fluids as derived by M Slemrod(1984) and J E Dunn and J Serrin(1985). We establish the existence, uniqueness and exponential stability of global solutions in H^2×H^1× H^1 for the one-dimensional Navier-Stokes-Korteweg equations by a priori estimates,which implies the existence and exponential stability of the nonlinear C_0-semigroups S(t) on H^2× H^1× H^1.
In this paper, we investigate non-isothermal one-dimensional model of capillary compressible fluids as derived by M Slemrod（1984） and J E Dunn and J Serrin（1985）. We establish the existence, uniqueness and exponential stability of global solutions in H^2×H^1× H^1 for the one-dimensional Navier-Stokes-Korteweg equations by a priori estimates,which implies the existence and exponential stability of the nonlinear C_0-semigroups S（t） on H^2× H^1× H^1.
基金
Supported by the National Natural Science Foundation of China(11271066)
Supported by the Shanghai Education Commission(13ZZ048)
