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

2025/10/23 by Feireisl, Eduard, Neves, Wladimir
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.20316

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.

Citations

• On the Rayleigh--B' enard convection problem for rotating fluids
• Unconditional stability of equilibria in thermally driven compressible fluids
• Super-exponential convergence rate of a nonlinear continuous data assimilation algorithm: The 2D Navier-Stokes equations paradigm
• Turbulent Rotating Rayleigh–Bénard Convection
• Navier-Stokes-Fourier system with Dirichlet boundary conditions
• Determining Map, Data Assimilation and an Observable Regularity Criterion for the Three-Dimensional Boussinesq System
• Continuous Data Assimilation for the Three Dimensional Navier-Stokes\n Equations
• The Initialization of Numerical Models by a Dynamic-Initialization Technique

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