一维可压缩Navier-Stokes-Korteweg方程组的大初值整体光滑解
GLOBAL SMOOTH SOLUTIONS TO THE 1-D COMPRESSIBLE NAVIER-STOKES-KORTEWEG SYSTEM WITH LARGE INITIAL DATA

本文研究了当粘性系数和毛细系数是密度函数的一般光滑函数时，一维等温的可压缩NavierStokes-Korteweg方程的Cauchy问题.利用基本能量方法和Kanel的技巧，得到了大初值、非真空光滑解的整体存在性与时间渐近行为.本文结果推广了已有文献中的结论.
This paper is concerned with the Cauchy problem of the one-dimensional isothermal compressible Navier-Stokes-Korteweg system when the viscosity coe-cient and capillarity coe-cient are general smooth functions of the density. By using the elementary energy method and Kanel's technique[25], we obtain the global existence and time-asymptotic behavior of smooth non-vacuum solutions with large initial data, which improves the previous ones in the literature