On the properties in solutions of the Shrira equation

In this paper we establish the propagation of regularity phenomena for solutions of the initial-value problem (IVP) associated to the Shrira equation, a two-dimensional model appearing in shear flows. We prove that if initial data has some prescribed regularity on the right hand side of the real line, then this regularity is propagated with infinite speed by the flow solution. In other words, the extra regularity on the data propagates in the solutions in the direction of the dispersion. A similar result is also obtained for a model arising in the study of capillary-gravity flows.