论文标题
真空附近不均匀动力学方程的全球适应性和稳定性
Global well-posedness and stability of the inhomogeneous kinetic wave equation near vacuum
论文作者
论文摘要
在本文中，我们证明了在4波无与伦比的动力学波动方程的真空附近的时代存在，唯一性和稳定性，用于尺寸laplacian分散性关系$ d = 2,3 $。我们还表明，对于非负初始数据，该解决方案仍然是非负的。这是通过将不均匀的动力学方程与具有中等硬势且无碰撞平均的量子玻尔兹曼型方程的立方部分连接到量子玻尔兹曼型方程的立方部分来实现的。
In this paper, we prove global in time existence, uniqueness and stability of mild solutions near vacuum for the 4-wave inhomogeneous kinetic wave equation, for Laplacian dispersion relation in dimension $d=2,3$. We also show that for non-negative initial data, the solution remains non-negative. This is achieved by connecting the inhomogeneous kinetic wave equation to the cubic part of a quantum Boltzmann-type equation with moderately hard potential and no collisional averaging.
