Average Regularity of the Solution to an Equation with the Relativistic-free Transport Operator

Jianjun Huang, Zhenglu Jiang

Let $u=u(t,\mathbf{x},\mathbf{p})$ satisfy the transport equation $\frac{\partial u}{\partial t}+\frac{\mathbf{p}}{p_0}\frac{\partial u}{\partial \mathbf{x}}=f$, where $f=f(t,\mathbf{x},\mathbf{p})$ belo…