Effective weak universality in short intervals

We prove an effective multidimensional $\Omega$-result of Voronin in short intervals $[T,T+H]$ with $T^{\frac{27}{82}}\le H\le T$, and derive an effective weak universality theorem of the Riemann zeta-function. Furthermore, we provide a few remarks for these results under the assumption of the Riemann hypothesis.