Control estimates for 0th order pseudodifferential operators

We introduce the control conditions for 0th order pseudodifferential operators \mathbf{P} whose real parts satisfy the Morse--Smale dynamical condition. We obtain microlocal control estimates under the control conditions. As a result, we show that there are no singular profiles in the solution to the evolution equation (i\partial_t-\mathbf{P})u=f when \mathbf{P} has... Show more