Well-posedness and ill-posedness for a fifth-order shallow water wave equation Original Research Article

In this paper we establish a new bilinear estimate in suitable Bourgain spaces by using a fundamental estimate on dyadic blocks for the Kawahara equation which was obtained by the [k;Z][k;Z] multiplier norm method of Tao (2001) [2]; then the local well-posedness of the Cauchy problem for a fifth-order shallow water wave equation in View the MathML sourceHs(R) with View the MathML sources>−54 is obtained by the Fourier restriction norm method. And some ill-posedness in View the MathML sourceHs(R) with View the MathML sources<−54 is derived from a general principle of Bejenaru and Tao.