2024/03/13 by Lei Yao, Lei, Yao, Haiyan, Yin +2
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2403.09730
openalex publication_date 2024/03/13 · openalex created_date 2024/03/19 · openalex updated_date 2026/07/28
The main concern of this paper is to study large-time behavior of the sheath to the full Euler-Poisson system. As is well known, the monotone stationary solution under the Bohm criterion can be referred to as the sheath which is formed by interactions of plasma with wall. So far, the existence and asymptotic stability of stationary solutions in one-dimensional half space to the full Euler-Poisson system have been proved in \citeDYZ2021. In the present paper, we extend the results in \citeDYZ2021 to N-dimensional (N=1,2,3) half space. By assuming that the velocity of the positive ion satisfies the Bohm criterion at the far field, we establish the global unique existence and the large time asymptotic stability of the sheath in some weighted Sobolev spaces by weighted energy method. Moreover, the time-decay rates are also obtained. A key different point from \citeDYZ2021 is to derive some boundary estimates on the derivative of the potential in the x1-direction.