LITTLEWOOD–PALEY THEORY AND REGULARITY ISSUES IN BOLTZMANN HOMOGENEOUS EQUATIONS I: NON-CUTOFF CASE AND MAXWELLIAN MOLECULES
LITTLEWOOD–PALEY THEORY AND REGULARITY ISSUES IN BOLTZMANN HOMOGENEOUS EQUATIONS I: NON-CUTOFF CASE AND MAXWELLIAN MOLECULES
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DOI：
10.1142/s0218202505000613
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发表时间：
2005-06
影响因子：
3.5
通讯作者：
Radjesvarane Alexandre;Mouhamad El Safadi
中科院分区：
文献类型：
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作者：
Radjesvarane Alexandre;Mouhamad El Safadi
我们使用 Littlewood-Paley 理论来分析齐次玻尔兹曼方程解的正则化性质。对于非截止麦克斯韦分子，我们表明这样的解比初始数据更平滑。尽管 Desvillettes 和 Wennberg10 最近的最新结果对碰撞横截面做出了更一般的假设，但我们的方法似乎比之前用于显示此类属性的方法更简单，并且也适用于任何弱解决方案。
We use Littlewood–Paley theory for the analysis of regularization properties of solutions of the homogeneous Boltzmann equation. For non-cutoff Maxwellian molecules, we show that such solutions are smoother than the initial data. Although the recent and up to date results of Desvillettes and Wennberg10 assume much more general assumptions on the collision cross sections, our method seems to be simpler than those used earlier to show such properties and also applies to any weak solution.