LARGE TIME BEHAVIOR OF THE 1D ISENTROPIC NAVIER-STOKES-POISSON SYSTEM

doi:10.1007/s10473-022-0509-x

Abstract

Abstract: The initial value problem (IVP) for the one-dimensional isentropic compressible Navier-Stokes-Poisson (CNSP) system is considered in this paper. For the variables, the electric field and the velocity, under the Lagrange coordinate, we establish the global existence and uniqueness of the classical solutions to this IVP problem. Then we prove by the method of complex analysis, that the solutions to this system converge to those of the corresponding linearized system in the L² norm as time tends to infinity. In addition, we show, using Green’s function, that the solutions to this system are close to a diffusion profile, pointwisely, as time goes to infinity.

Key words: 1D Navier-Stokes-Poisson system, well-posedness, L²-time decay rates, time-space pointwise behaviors

CLC Number:

35M10

Qingyou He, Jiawei Sun. LARGE TIME BEHAVIOR OF THE 1D ISENTROPIC NAVIER-STOKES-POISSON SYSTEM[J].Acta mathematica scientia,Series B, 2022, 42(5): 1843-1874.

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