Stability of a nonlinear wave for an outflow problem of the bipolar quantum Navier-Stokes-Poisson system. (English) Zbl 07877975
Summary: In this paper, we shall investigate the large-time behavior of the solution to an outflow problem of the one-dimensional bipolar quantum Navier-Stokes-Poisson system in the half space. Under some suitable assumptions on the boundary data and the space-asymptotic states, we successfully construct a nonlinear wave which is the superposition of the stationary solution and the 2-rarefaction wave. Then, by means of the \(L^2\)-energy method, we prove that this nonlinear wave is asymptotically stable provided that the initial perturbation and the strength of the stationary solution are small enough, while the strength of the 2-rarefaction wave can be arbitrarily large.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q40 | PDEs in connection with quantum mechanics |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76E25 | Stability and instability of magnetohydrodynamic and electrohydrodynamic flows |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
| 76Y05 | Quantum hydrodynamics and relativistic hydrodynamics |
| 78A35 | Motion of charged particles |
| 82D37 | Statistical mechanics of semiconductors |
| 35B40 | Asymptotic behavior of solutions to PDEs |
Keywords:
bipolar quantum Navier-Stokes-Poisson system; outflow problem; large-time behavior; stationary solution; 2-rarefaction waveReferences:
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