Control estimates for 0th order pseudodifferential operators
| Autor: | Christianson, Hans, Wang, Jian, Wang, Ruoyu P. T. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 20 pages, 3 figures. To appear in Int. Math. Res. Not. IMRN |
| Databáze: | arXiv |
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