The decay rate of solution for the bipolar Navier-Stokes-Poisson system (Q2924870)

In this paper the authors investigate the time-asymptotic behavior of solutions for the Cauchy problem for the bipolar Navier-Stokes-Poisson system. They are able to prove the global existence and the \(H^{s}\) decay rate of classical solutions for this problem. The proof uses mainly the analysis of Green's function of the corresponding linearized system and certain elaborate energy estimates. With the aid of the \(H^{s}\) decay rate of the solutions a \(L^{p}\) estimate of the solution can also be given. To obtain the decay rates of the higher order derivatives of solutions, the authors perform a short wave-long wave decomposition of solutions. The article is self-contained and it presents a good survey on the topic and its history.