On the Global Existence of Mild Solutions to the Boltzmann Equation for Small Data in LD
On the Global Existence of Mild Solutions to the Boltzmann Equation for Small Data in LD
复制标题
LD小数据玻尔兹曼方程温和解的全局存在性
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Diogo Arsénio
中科院分区：
文献类型：
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作者：
Diogo Arsénio
提出了小初始数据下玻尔兹曼方程全局解存在性的新理论。这些新的温和解类似于Navier-Stokes方程的温和解。这种存在是由于研究了由输运算子引起的色散和由非线性玻尔兹曼碰撞算子引起的奇点形成的竞争现象。正是将所谓的色散估计与碰撞算子增益项上的新卷积不等式联合使用，才能得到解的一致界，从而证明解的存在性。
We develop a new theory of existence of global solutions to the Boltzmann equation for small initial data. These new mild solutions are analogous to the mild solutions for the Navier-Stokes equations. The existence comes as a result of the study of the competing phenomena of dispersion, due to the transport operator, and of singularity formation, due to the nonlinear Boltzmann collision operator. It is the joint use of the so-called dispersive estimates with new convolution inequalities on the gain term of the collision operator that allows to obtain uniform bounds on the solutions and thus demonstrate the existence of solutions.