论文标题
全球薄弱的解决方案，用于无抗汉堡 - vlasov方程
Global weak solutions to inviscid Burgers-Vlasov equations
论文作者
论文摘要
在本文中，我们考虑了一个尺寸流体粒子相互作用模型的全球弱解决方案：Inviscid Burgers-Vlasov方程，其流体速度为$ l^\ infty $，而粒子的概率密度则以$ l^1 $。我们的弱解决方案也是一个熵解决方案，以使汉堡的方程式无关。该方法是增加了巧妙的人工粘度，以构建满足$ l^\ infty $补偿紧凑型框架和弱$ l^1 $紧凑型框架的近似解决方案。值得指出的是，流体速度和颗粒概率密度的动能的边界都独立于时间。
In this paper, we consider the existence of global weak solutions to a one dimensional fluid-particles interaction model: inviscid Burgers-Vlasov equations with fluid velocity in $L^\infty$ and particles' probability density in $L^1$. Our weak solution is also an entropy solution to inviscid Burgers' equation. The approach is adding ingeniously artificial viscosity to construct approximate solutions satisfying $L^\infty$ compensated compactness framework and weak $L^1$ compactness framework. It is worthy to be pointed out that the bounds of fluid velocity and the kinetic energy of particles' probability density are both independent of time.
