Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential
Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential
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具有库仑势的齐次 Landau 方程径向解的估计
DOI：
10.2140/apde.2016.9.1772
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Nestor Guillen
中科院分区：
文献类型：
--
作者：
M. Gualdani;Nestor Guillen
受全局解存在性问题的驱动，我们得到了具有库仑势的齐次朗道方程的径向对称且单调的解的逐点上界。这些估计表明，在有限时间\(T\)时\(L^{\infty}\)范数下的爆破只有当解的\(L^{3/2}\)范数在接近\(T\)的时刻集中时才会发生。这些界是通过使用朗道方程以及相关质量函数的比较原理得到的。
这种方法为最近由克里格（Krieger）和斯特兰（Strain）提出的具有库仑势的朗道方程的各向同性形式提供了长时间存在性结果。
Motivated by the question of existence of global solutions, we obtain pointwise upper bounds for radially symmetric and monotone solutions to the homogeneous Landau equation with Coulomb potential. The estimates say that blow up in the $L^\infty$-norm at a finite time $T$ can occur only if the $L^{3/2}$-norm of the solution concentrates for times close to $T$. The bounds are obtained using the comparison principle for the Landau equation and for the associated mass function.
This method provides long-time existence results for the isotropic version of the Landau equation with Coulomb potential, recently introduced by Krieger and Strain.