摘要
We consider the Cauchy problem for the three-dimensional bipolar compressible Navier-Stokes-Poisson system with unequal viscosities.Under the assumption that the H_(3) norm of the initial data is small but its higher order derivatives can be arbitrarily large,the global existence and uniqueness of smooth solutions are obtained by an ingenious energy method.Moreover,if additionally,the H^(−s)(1/2≤s<3/2)or B^(−s)_(2,∞)(1/2<s≤3/2)norm of the initial data is small,the optimal decay rates of solutions are also established by a regularity interpolation trick and delicate energy methods.
基金
supported by National Natural Science Foundation of China(Grant Nos.11701193 and 11671086)
Natural Science Foundation of Fujian Province(Grant No.2018J05005)
the Scientific Research Funds of Huaqiao University(Grant No.16BS507)
supported by Guangxi Natural Science Foundation(Grant No.2019JJG110003)
Guangxi Science and Technology Plan Project(Grant No.2019AC20214)
National Natural Science Foundation of China(Grant Nos.11771150,11571280,11301172 and 11226170).