Data Assimilation to the Primitive Equations with $L^p$-$L^q$-based Maximal Regularity Approach

In this paper, we show mathematical justification of the data assimilation of nudging type in $L^p$-$L^q$ maximal regularity settings. We prove that the approximate solution of the primitive equations by data assimilation converges to the true solution with exponential order on the Besov space $B^{2/q}_{q,p}(\Omega)$ in the periodic layer domain $\Omega = \mathbb{T}^2 \times (-h, 0)$.