Well-posedness of the Cauchy problem for the fractional power dissipative equations

Changxing Miao, Baoquan Yuan, Bo Zhang

This paper studies the Cauchy problem for the nonlinear fractional power dissipative equation $u_t+(-△{)}^{\alpha }u=F(u)$ for initial data in the Lebesgue space $L^r(\mr^n)$ with $…