Continuous data assimilation applied to the Rayleigh-Benard problem for compressible fluid flows

TL;DR

This paper demonstrates the effectiveness of a continuous data assimilation method in accurately tracking the behavior of compressible, rotating, and thermally driven fluid flows governed by the Navier-Stokes-Fourier system, especially in low Mach and high Rossby and Froude number regimes.

Contribution

It provides a rigorous proof of the tracking property for the data assimilation method applied to complex compressible fluid models under realistic large data conditions.

Findings

Proves the tracking property in low Mach, high Rossby and Froude regimes.

Handles large data within the weak solution framework.

Validates the method's applicability to complex fluid systems.

Abstract

We apply a continuous data assimilation method to the Navier-Stokes-Fourier system governing the evolution of a compressible, rotating and thermally driven fluid. A rigorous proof of the tracking property is given in the asymptotic regime of low Mach and high Rossby and Froude numbers. Large data in the framework of weak solutions are considered.