论文标题
$ l^p_β$ -norm的繁殖，$ 1 <p \ le \ infty $，用于玻尔兹曼方程的系统，用于单变性气体混合物
Propagation of $L^p_β$-norm, $ 1<p\le \infty$, for the system of Boltzmann equations for monatomic gas mixtures
论文作者
论文摘要
对于完整的非线性均匀型玻尔兹曼方程式的矢量值解决方案的存在和唯一性，描述了用于二元相互作用的多组分子模子气体混合物的方程式[8]，我们在此手稿中介绍了该解决方案的几种属性。我们首先证明了多物种碰撞运算符的增益项的可集成性增长，从而扩展了先前针对单个物种情况所做的工作[3]。此外，我们研究了多种碰撞操作员作为双线性形式的可集成性特性，重新审视和扩展了单个气体所做的工作[2]。与[8]中的碰撞运算符的损失项一起，以及下面的控制，我们开发了多项式和指数$β$加权的$ l^p_β$ - 矢量值解决方案的传播。最后，我们将这种$ l^p_β$ -norms的传播属性扩展到$ p = \ infty $。
With the existence and uniqueness of a vector value solution for the full non-linear homogeneous Boltzmann system of equations describing multi-component monatomic gas mixtures for binary interactions proved [8], we present in this manuscript several properties for such a solution. We start by proving the gain of integrability of the gain term of the multispecies collision operator, extending the work done previously for the single species case [3]. In addition, we study the integrability properties of the multispecies collision operator as a bilinear form, revisiting and expanding the work done for a single gas [2]. With these estimates, together with a control by below for the loss term of the collision operator as in [8], we develop the propagation for the polynomially and exponentially $β$-weighted $L^p_β$-norms for the vector value solution. Finally, we extend such $L^p_β$-norms propagation property to $p=\infty$.
