Global existence of solutions for the Cauchy problem of the Kawahara equation with L2 initial data

In this paper we study solvability of the Cauchy problem of the Kawahara equation partial derivative(t)u + au partial derivative(x)u + beta partial derivative(3)(x)u + gamma partial derivative(5)(x)u = 0 with L-2 initial data. By working on the Bourgain space X-r,X-s(R-2) associated with this equation, we prove that the Cauchy problem of the Kawahara equation is locally solvable if initial data belong to Hr(R) and -1 < r < 0. This result combined with the energy conservation law of the Kawahara equation yields that global solutions exist if initial data belong to L-2 (R).