A quasineutral type limit for the Navier–Stokes–Poisson system with large data

Abstract

In this paper we investigate a quasineutral type limit for the Navier-Stokes-Poisson system. We prove that the projection of the approximating velocity fields on the divergence-free vector field is relatively compact and converges to a Leray weak solution of the incompressible Navier-Stokes equation. By exploiting the wave equation structure of the density fluctuation we achieve the convergence of the approximating sequences by means of a dispersive estimate of the Strichartz type.

Dispersive behaviour in the analysis of acoustic waves and plasma oscillations

“…In the last years the quasineutral limit for hydrodynamical models of plasma or semiconductor devices has been widely studied by many authors, in the case of Euler Poisson system, or in the case of the Navier Stokes Poisson system with well-prepared initial data, or ill prepared data and smooth solutions and also in the contest of the combined quasineutral and inviscid limit, see for instance the papers [4], [5], [6], [7], [8], [11], [15], [16], [20], [25]. In particular in [8] the authors investigated the quasineutral limit of the isentropic Navier-StokesPoisson system in the whole space and obtained the convergence of weak solution of the Navier-Stokes-Poisson system to the weak solution of the incompressible Navier-Stokes equations by under the assumption that the Mach number is related to the Debye length.…”

“…In particular in [8] the authors investigated the quasineutral limit of the isentropic Navier-StokesPoisson system in the whole space and obtained the convergence of weak solution of the Navier-Stokes-Poisson system to the weak solution of the incompressible Navier-Stokes equations by under the assumption that the Mach number is related to the Debye length.…”

Convergence of the Navier–Stokes–Poisson system to the incompressible Navier–Stokes equations

“…8, where the convergence of weak solution of the NSP system to the weak solution of the incompressible Navier-Stokes equations is obtained under the assumption that the Mach number is related to the Debye length. Noticing that our result is different from that in Ref.…”

Regularity and asymptotic behavior of 1D compressible Navier–Stokes–Poisson equations with free boundary

“…For more works about NavierStokes-Poisson equations, such as global existence of small disturbance solution, pointwise estimates and limit problem for the Cauchy problem, etc., please see [1,5,8,16,26,27] and references therein. There is also important progress recently on the existence of local and global weak solutions (re-normalized solution), one can refer to [4,6,7].…”