Data assimilation for the barotropic Navier-Stokes system

TL;DR

This paper develops a continuous data assimilation method for the barotropic Navier-Stokes system, demonstrating complete synchronization of observed and numerical solutions under suitable parameters.

Contribution

It introduces a data assimilation approach that ensures synchronization for the barotropic Navier-Stokes system using dissipative solutions and nudging parameters.

Findings

Complete synchronization achieved on any compact interval

Synchronization depends on appropriate nudging parameters

Method applies to dissipative solutions, broader than weak solutions

Abstract

We consider a continuous data assimilation method for the barotropic Navier--Stokes system. The observed solution is supposed to be bounded on the whole time period of observation, while the synchronized solution, usually provided by a numerical method, belongs to the class of dissipative solutions that is considerably larger than the class of conventional weak solutions. A complete synchronization is shown on any compact prediction interval provided the nudging parameters are chosen appropriately.