摘要
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.
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.
基金
Supported by the Research Grant of Department of Education of Hubei Province(Q20142803)
