An explicit time for the uniform null controllability of a linear Korteweg-de Vries equation

In this paper, we consider a linear Korteweg-de Vries equation posed in a bounded interval and study the time dependency with respect to the interval length and the transport coefficient, for which the uniform null controllability holds as the dispersion coefficient goes to zero. We consider two cases of boundary controls. First, only one control on the left end of the interval, and then, two controls acting on the right. The strategy is based on the combination of an exponential dissipation inequality and suitable Carleman estimates for each case.