Global Existence for a Nonlinear System with Fractional Laplacian in Banach Space

Miguel Loayza, Paulo R. F. S. Silva

We consider the cauchy problem for the fractional power dissipative equation $u_t+(-\Delta {)}^{\beta /2}u=F(u)$, where $\beta >0$ and $F(u)=B(u,...,u)$ and $B$ is a multilinear form on a Banach s…