Communications in Mathematical Sciences
Volume 12 (2014)
Decay of the solution for the bipolar Euler-Poisson system with damping in dimension three
Pages: 1257 – 1276
The global solution to Cauchy’s problem of the bipolar Euler-Poisson equations with damping in dimension three are constructed when the initial data in $H^3$ norm is small. Moreover, by using a refined energy estimate together with the interpolation trick, we improve the decay estimate in [Y.P. Li and X.F. Yang, J. Diff. Eqs., 252(1), 768–791, 2012], and we need not the smallness assumption of the initial data in L1 space in [Y.P. Li and X.F. Yang, J. Diff. Eqs., 252(1), 768–791, 2012].
bipolar Euler-Poisson system, global existence, decay estimates, negative Sobolev’s space, negative Besov’s space
2010 Mathematics Subject Classification
35A01, 35B40, 35Q35