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arXiv · 2303.06443

Control estimates for 0th order pseudodifferential operators

Hans Christianson·Jian Wang·Ruoyu P. T. Wang
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Abstract

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 a damping term that satisfies the control condition and $f\in C^{\infty}$. This is motivated by the study of a microlocal model for the damped internal waves.

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Hans Christianson, Jian Wang, Ruoyu P. T. Wang. 2023-03-11. Control estimates for 0th order pseudodifferential operators. https://arxiv.org/abs/2303.06443

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