Abstract
We consider the zero-electron-mass limit for the Navier–Stokes–Poisson system in unbounded spatial domains. Assuming smallness of the viscosity coefficient and ill-prepared initial data, we show that the asymptotic limit is represented by the incompressible Navier–Stokes system, with a Brinkman damping, in the case when viscosity is proportional to the electron-mass, and by the incompressible Euler system provided the viscosity is dominated by the electron mass. The proof is based on the RAGE theorem and dispersive estimates for acoustic waves, and on the concept of suitable weak solutions for the compressible Navier–Stokes system.
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Acknowledgements
The work of E.F. was supported by Grant 201/09/0917 of GA ČR as a part of the general research programme of the Academy of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503.
The work of A.N. was partially supported by the general research programme of the Academy of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503.
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Communicated by Robert V. Kohn.
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Donatelli, D., Feireisl, E. & Novotný, A. On the Vanishing Electron-Mass Limit in Plasma Hydrodynamics in Unbounded Media. J Nonlinear Sci 22, 985–1012 (2012). https://doi.org/10.1007/s00332-012-9134-5
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DOI: https://doi.org/10.1007/s00332-012-9134-5