Communications in Mathematical Sciences

Volume 12 (2014)

Number 7

Decay of the solution for the bipolar Euler-Poisson system with damping in dimension three

Pages: 1257 – 1276

DOI: https://dx.doi.org/10.4310/CMS.2014.v12.n7.a5

Authors

Zhigang Wu (Department of Applied Mathematics, College of Science, Donghua University, Shanghai, China)

Weike Wang (Department of Mathematics, Shanghai Jiao Tong University, Shanghai, China)

Abstract

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].

Keywords

bipolar Euler-Poisson system, global existence, decay estimates, negative Sobolev’s space, negative Besov’s space

2010 Mathematics Subject Classification

35A01, 35B40, 35Q35

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Published 14 May 2014