Convergence of the three-dimensional compressible Navier-Stokes-Poisson-Korteweg equation to the incompressible Euler equation

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• 作者：Fang Zhou
• 关键词：Navier ; Stokes ; Poisson ; Korteweg equation ; incompressible Euler equation ; smooth solution ; energy ; type error estimate
• 刊名：Wuhan University Journal of Natural Sciences
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：22
• 期：1
• 页码：19-28
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Life Sciences, general; Materials Science, general; Computer Science, general;
• 出版者：Wuhan University
• ISSN：1993-4998
• 卷排序：22

文摘

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.