无限真空中含外力的Enskog方程的整体解
Global Solution to Enskog Equation with External Force in Infinite Vacuum
摘要：
首先给出了与具有外力的Enskog方程相对应的双特征方程的假设。由于Enskog方程的碰撞算子比Boltzmann方程的复杂，这些假设比Duan等人对Boltzmann方程给出的假设更复杂。这些假设与中密度或高密度气体粒子沿双特征曲线的碰撞密切相关，并可用来估计Enskog积分方程的增益积分和损失积分。然后，通过控制这些积分，我们证明了在无限真空中的中等或高密度气体的Enskog方程的整体温和解的存在性和唯一性。最后，我们对Enskog方程中碰撞因子的局部Lipschitz假设作了一些评论。
英文摘要：
We first give hypotheses of the bicharacteristic equations corresponding to the Enskog equation with an external force. Since the collision operator of the Enskog equation is more complicated than that of the Boltzmann equation, these hypotheses are more complicated than those given by Duan et al. for the Boltzmann equation. The hypotheses are very related to collision of particles of moderately or highly dense gases along the bicharacteristic curves and they can be used to make the estimation of the so-called gain and loss integrals of the Enskog integral equation. Then, by controlling these integrals, we show the existence and uniqueness of the global mild solution to the Enskog equation in an infinite vacuum for moderately or highly dense gases. Finally, we make some remarks on the locally Lipschitz assumption of the collision factors in the Enskog equation.
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