Stability of the superposition of boundary layer and rarefaction wave for outflow problem on the two-fluid Navier–Stokes–Poisson system. (October 2016)

• Record Type: Journal Article
• Authors: Yin, Haiyan; Zhang, Jinshun; Zhu, Changjiang
• Is Part Of: Nonlinear analysis. Volume 31(2016)
• Page Start: 492
• Page End: 512
• Publication Date: 2016-10
• Subjects: Navier–Stokes–Poisson -- Boundary layer and rarefaction wave -- Stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.01.020
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is concerned with the study of nonlinear stability of superposition of boundary layer and rarefaction wave on the two-fluid Navier–Stokes–Poisson system in the half line R + = : ( 0, + ∞ ) . On account of the quasineutral assumption and the absence of the electric field for the large time behavior, we successfully construct the boundary layer and rarefaction wave, and then we give the rigorous proofs of the stability theorems on the superposition of boundary layer and rarefaction wave under small perturbations for the corresponding initial boundary value problem of the Navier–Stokes–Poisson system, only provided the strength of boundary layer is small while the strength of rarefaction wave can be arbitrarily large. The complexity of nonlinear composite wave leads to many complicated terms in the course of establishing the a priori estimates. The proofs are given by an elementary L 2 energy method.