TY - JOUR

T1 - Fluid mechanical approximation to the degenerated drift-diffusion system from the compressible Navier-Stokes-Poisson system

AU - Kobayashi, Takayuki

AU - Ogawa, Takayoshi

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We consider the zero relaxation time approximation to the compressible Navier-Stokes-Poisson system to derive the mono-polar drift-diffusion system of degenerated type. To construct the approximation solution, we introduce a regularized, damped, viscous, compressible Navier-Stokes-Poisson equation; as the relaxation time τ → 0, the weak solution converges to that of the degenerated elliptic parabolic system. The entropy functional is rigorously derived from the energy inequality of the approximation system. We employ the argument developed in the theory of weak solutions in the compressible Navier-Stokes-Poisson system with the regularized pressure.

AB - We consider the zero relaxation time approximation to the compressible Navier-Stokes-Poisson system to derive the mono-polar drift-diffusion system of degenerated type. To construct the approximation solution, we introduce a regularized, damped, viscous, compressible Navier-Stokes-Poisson equation; as the relaxation time τ → 0, the weak solution converges to that of the degenerated elliptic parabolic system. The entropy functional is rigorously derived from the energy inequality of the approximation system. We employ the argument developed in the theory of weak solutions in the compressible Navier-Stokes-Poisson system with the regularized pressure.

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U2 - 10.1512/iumj.2013.62.5017

DO - 10.1512/iumj.2013.62.5017

M3 - Article

AN - SCOPUS:84904463246

VL - 62

SP - 1021

EP - 1054

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

IS - 3

ER -