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 $B_{q,p}^{2\mathrm{/}q}(\mathrm{\Omega })$ in the periodic layer domain $\mathrm{\Omega }={\mathbb{T}}^2\times (-h,0)$.