Global existence and spatial analyticity for a nonlocal flux with fractional diffusion

Yu Gao, Cong Wang, Xiaoping Xue

In this paper, we study a one dimensional nonlinear equation with diffusion $-\nu (-{\partial }_{xx}{)}^{\frac{\alpha }{2}}$ for $0\le \alpha \le 2$ and $\nu >0$. We use a viscous-splitting algorithm to…