Asymptotically self-similar shock formation for 1d fractal Burgers equation

Kyle R. Chickering, Ryan C. Moreno-Vasquez, Gavin Pandya

For $0<\alpha <\frac{1}{3}$ we construct unique solutions to the fractal Burgers equation ${\partial }_{t}u+u{\partial }_{x}u+(-\Delta {)}^{\alpha }u=0$ which develop a first shock in finite time, starting…