The Cauchy Problem for a Fifth-Order Dispersive Equation - Hongjun Wang; Yongqi Liu; Yongqiang Chen (Abstract and Applied Analysis)
This paper is devoted to studying the Cauchy problem for a fifth-order equation. We prove that it is locally well-posed for the initial data in the Sobolev space Hs(R) with s≥1/4. We also establish the ill-posedness for the initial data in Hs(R) with s<1/4. Thus, the regularity requirement for the fifth-order dispersive equations s≥1/4 is sharp.