This paper concerns the initial-boundary value problem of the Kawahara equation posed on the right and left half-lines. We prove the local well-posedness in the low regularity Sobolev space. We introduce the Duhamel boundary forcing operator, which is introduced by Colliander and Kenig (Commun Partial Differ Equ 27:2187–2266, 2002) in the context of Airy group operators, to construct solutions on the whole line. We also give the bilinear estimate in \(X^{s,b}\) space for \(b < \frac{1}{2}\), which is almost sharp compared to IVP of Kawahara equation (Chen et al. in J Anal Math 107:221–238, 2009; Jia and Huo in J Differ Equ 246:2448–2467, 2009).

本文涉及左右半线上的Kawahara方程的初边值问题。我们证明了低规则Sobolev空间中的局部适定性。我们介绍了Duhamel边界强制算子，它是在Airy群算子的上下文中由Colliander和Kenig引入的（Commun Partial Differ Equ Equ 27：2187–2266，2002），以构造整行的解。我们还给出了\（b <\ frac {1} {2} \）在\（X ^ {s，b} \）空间中的双线性估计，与Kawahara方程的IVP相比，这几乎是尖锐的（Chen等。见J Anal Math 107：221–238，2009； Jia和Huo见J Differ Equ 246：2448–2467，2009）。