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*. arrayrlr uₜ+ₓ⁵ u+uₓ u t>0, \\ u (x, 0) &-2mm=u₀ (x), & array \} align* has a unique local solution in time in the Bourgain spaces X^s, 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.