| 等离子体中法流体动力学模型整体光滑解的大时间行为 |
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| 引用本文： | 杨建伟,楚斌,王术.等离子体中法流体动力学模型整体光滑解的大时间行为[J].黑龙江大学自然科学学报,2010,27(1). |
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| 作者姓名： | 杨建伟 楚斌 王术 |
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| 作者单位： | 1. 北京工业大学应用数理学院,北京,100124
2. 河南省医药学校,开封,475001 |
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| 基金项目： | 国家自然科学基金资助项目，北京工业大学第一届博士创新计划资助项目 |
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| 摘 要： | 通过引入热力学能量,研究了等离子体中多维等熵流体动力学模型Cauchy问题在Rd中当初始密度接近常数时,整体光滑解的大时间行为.该模型由电子密度和电流密度的守恒律方程组耦合上关于静电位势的Poisson方程而组成.运用经典的和高阶的能量方法证明了该模型的解当时间t→∞时指数地快速衰减到(常数的)稳态解,这个结果对非等熵的情形也是正确的.
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| 关 键 词： | 流体动力学模型 光滑解的整体存在性 指数稳定性 解的大时间行为 热力学能量 |
The large time behavior of global smooth solutions to the multidimensional hydrodynamic model for plasmas |
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| YANG Jian-wei,CHU Bin,WANG Shu.The large time behavior of global smooth solutions to the multidimensional hydrodynamic model for plasmas[J].Journal of Natural Science of Heilongjiang University,2010,27(1). |
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| Authors: | YANG Jian-wei CHU Bin WANG Shu |
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| Abstract: | The large time behavior of global smooth solutions of the Cauchy problem for the multidimensional isentropic hydrodynamic model for plasmas in Rd is studied under the assumption that the initial densities are close to a constant by introducing the thermodynamical energy. The model consists of the conservation laws for the electron density and the current density coupled to the Poisson equation for the electrostatic potential. Furthermore, it is proved that the particle densities converge exponentially fast to the constant steady state as t→∞ by using classic and higher-order energy method. Moreover, this conclusion is also correct to the non-isentropic case. |
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| Keywords: | hydrodynamic model global existence of smooth solutions exponential stability long-time behavior of solutions plasmas thermodynamical energy |
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