Regularity properties and dispersive blow-up for the fifth order Korteweg-de Vries equation on the line

In this work we prove that the initial value problem (IVP) for the fifth order Korteweg-de Vries equation {align*} . {array}{rlr} u_t+∂_x^5 u+u∂_x u&{-2mm}=0,& x∈ R,\; t>0,\\ u(x,0)&{-2mm}=u_0(x),& {array} \} {align*} has a unique local solution in time in the Bourgain spaces Xs,b for appropriate values of s and b. Besides we prove a regularity property concerning the nonlinear part of that solution. Finally, using the previous property we establish a dispersive blow-up result for global in time solutions of this IVP.