Fractional Burgers equation with singular initial condition

Tomasz Jakubowski, Grzegorz Serafin

We consider the fractional Burgers equation ${\Delta }^{\alpha /2}u+b\cdot \nabla (u|u{|}^{(\alpha -1)/\beta })$ on ${\mathbf{R}}^d$, $d\ge 2$, with {$\alpha \in (1,2)$ and} $\beta >1$ and prove the existence of a s…