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

Abstract

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