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Finding a Morawetz type inequality for $\partial ^2_t u = \Delta _p u$

I am currently investigating an equation that is : $$\partial ^2_t u = \Delta _{3/2} u,$$ where $u : \mathbb{R}_+ \times \mathbb{R}^d \to \mathbb{R}$ and $\Delta _{3/2}$ stands for the $3/2$-laplacian ...
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