Spectrum Analysis of Some Kinetic Equations

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• 作者：Tong Yang ; Hongjun Yu
• 刊名：Archive for Rational Mechanics and Analysis
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：222
• 期：2
• 页码：731-768
• 全文大小：707 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Electromagnetism, Optics and Lasers
  Mathematical and Computational Physics
  Complexity
  Fluids
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0673
• 卷排序：222

文摘

We analyze the spectrum structure of some kinetic equations qualitatively by using semigroup theory and linear operator perturbation theory. The models include the classical Boltzmann equation for hard potentials with or without angular cutoff and the Landau equation with \({\gamma\geqq-2}\). As an application, we show that the solutions to these two fundamental equations are asymptotically equivalent (mod time decay rate \({t^{-5/4}}\)) as \({t\to\infty}\) to that of the compressible Navier–Stokes equations for initial data around an equilibrium state.