Abstract:
In this talk we discuss about the initial-boundary value problem for the Schrödinger-Korteweg-de Vries system on the left and right half-line for a wide class of initial-boundary data, including the energy regularity H1(R±) × H1(R±) for initial data. Assuming homogeneous boundary conditions it is shown for positive coupling interactions that local solutions can be extended globally in time for initial data in the energy space; furthermore, for negative coupling interactions it was proved, for a certain class of regular initial data, the following result: if the respective solution does not exhibits finite time blow-up in H1(R−) × H1( R−), then the norm of the weighted space L2(R-, |x| dx) × L2(R-, |x| dx) blows-up at infinity time with super-linear rate, this is obtained by using a satisfactory algebraic manipulation of a new global virial type identity associated to the system. This is a joint work with Adán Corcho.