| 刘双乾;马 璇.Landau-Fermi-Dirac方程的整体经典解[J].数学年刊A辑,2012,33(1):39~ |
| Landau-Fermi-Dirac方程的整体经典解 |
| Global Classical Solutions to Landau-Fermi-Dirac Equation |
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| DOI： |
| 中文关键词: Landau-Fermi-Dirac 方程, 整体存在性, 非线性能量方法 |
| 英文关键词:Landau-Fermi-Dirac equation, Global existence, Nonlinear energy method |
| 基金项目: |
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| 中文摘要: |
| 研究了周期区域上平衡态附近Landau-Fermi-Dirac 方程的Cauchy问题. 利用宏观-微观分解以及局部的守恒律得到一致空间能量估计. 接着结合对非线性碰撞算子的细致估计, 推导了包含随时间演化的等价瞬时能量的非线性能量估计, 进而得到一致的先验估计. 最后通过局部存在性、一致的先验估计以及连续性技巧, 得到了Landau-Fermi-Dirac 方程平衡态附近整体光滑解的存在性. |
| 英文摘要: |
| This paper is devoted to the Cauchy problem for Landau-Fermi-Dirac equation near equilibrium on torus.The authors mainly use the macro-micro decomposition together with the local conservation laws to deduce the uniform spatialenergy estimate. Then by careful estimates on thenonlinear collision operator, the authors study some nonlinear energy estimates including the times evolution of equivalentinstant total energy to obtain some uniform a priori estimates. The global-in-time classical solutions nearequilibrium are constructed by combining the local existence, the uniform a priori estimates as well as the continuity argument. |
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