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Does anyone know what $ 1_\omega v $ means where $v \in L^2((0,T) \times \Omega )$ and $\omega \subset \subset \Omega$?

It should be an indicator function of $(t,x)$, but not sure how to interpret it...

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The product of $v$ for the characteristic function of $(0,T)\times\omega$?

Probably $1_{\omega}:(0,T)\times\Omega\to\mathbb{R}$ is the function defined by $$1_{\omega}(t,x)=\{1,\textrm{ for }x\in\omega, 0,\textrm{ for }x\in\Omega\setminus\omega\}.$$

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