Local well-posedness for Kawahara equation
Local well-posedness for Kawahara equation
We consider the Cauchy problem for the Kawahara equation, which is a fifth-order KdV equation. This paper establishes the local well-posedness with initial data given in the Sobolev space $H^s(\mathbb{R})$. Previously, Chen, Li, Miao, and Wu (2009) proved the local well-posedness for $s>-7/4$, which has been improved to $s \geq …