Uncertainty principles for a kinetic equation

We study unique continuation properties for a kinetic equation. We establish sufficient conditions on the interaction potential and on the behavior of the solution at the initial and terminal times that ensure the solution is identically zero. Our strategy adapts that of Escauriaza et al. (2006), combining the logarithmic convexity of certain quantities—which yields quadratic exponential decay at infinity of the solution—with a suitable Carleman inequality, which provides a lower bound for the $ L^2 $-norm of the solution in an appropriate annular domain.