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 with . We also establish the ill-posedness for the initial data in with . Thus, the regularity requirement for the fifth-order dispersive equations is sharp.
Hongjun Wang. Yongqi Liu. Yongqiang Chen. "The Cauchy Problem for a Fifth-Order Dispersive Equation." Abstr. Appl. Anal. 2014 (SI43) 1 - 8, 2014. https://doi.org/10.1155/2014/404781