  In this paper, we consider the well-posedness for the Cauchy problem of the
Kawahara equation with low regularity data in the periodic case. We obtain the
local well-posedness for $s \geq -3/2$ by a variant of the Fourier restriction
norm method. On the other hand, we show the ill-posedness for $s <-3/2$ in weak
sense. Moreover, the local solutions can be extended globally in time for $s
\geq -1$ by the I-method. This is a shape contrast to the results in the
non-periodic setting, where the critical exponent is equal to -2.
