Abstract
We study the combination of quasi-neutral limit and viscosity limit of smooth solution for the three-dimensional compressible viscous Navier-Stokes-Poisson-Korteweg equation for plasmas and semiconductors. When the Debye length and viscosity coefficients are sufficiently small, the initial value problem of the model has a unique smooth solution in the time interval where the corresponding incompressible Euler equation has a smooth solution. We also establish a sharp convergence rate of smooth solutions for three-dimensional compressible viscous Navier-Stokes-Poisson-Kortewe equation towards those for the incompressible Euler equation in combining quasi-neutral limit and viscosity limit. Moreover, if the incompressible Euler equation has a global smooth solution, the maximal existence time of three-dimensional compressible Navier-Stokes-Poisson-Korteweg equation tends to infinity as the Debye length and viscosity coefficients goes to zero.
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Foundation item: Supported by the Research Grant of Department of Education of Hubei Province (Q20142803)
Biography: ZHOU Fang, female, Associate professor, research direction: partial differential equations.
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Zhou, F. Convergence of the three-dimensional compressible Navier-Stokes-Poisson-Korteweg equation to the incompressible Euler equation. Wuhan Univ. J. Nat. Sci. 22, 19–28 (2017). https://doi.org/10.1007/s11859-017-1212-y
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DOI: https://doi.org/10.1007/s11859-017-1212-y
Keywords
- Navier-Stokes-Poisson-Korteweg equation
- incompressible Euler equation
- smooth solution
- energy-type error estimate