The Cauchy Problem for a Fifth-Order Dispersive Equation

Abstract EN

This paper is devoted to studying the Cauchy problem for a fifth-orderequation.

We prove that it is locally well-posed for the initial data in the Sobolevspace H s ( R ) with s ≥ 1 / 4 .

We also establish the ill-posedness for the initial data in H s ( R ) with s < 1 / 4 .

Thus, the regularity requirement for the fifth-order dispersive equations s ≥ 1 / 4 is sharp.