Transverse asymptotic stability of line solitary waves for the Ionic Euler-Poisson system

Abstract

We prove the linear and nonlinear asymptotic stability of small amplitude one-dimensional solitary waves submitted to small localized irrotational perturbations in the three dimensional Euler-Poisson system describing the dynamics of ions. In particular, in this regime, we obtain the existence of global smooth solutions and describe their asymptotic behavior.

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