In most results concerning bounds on the heat transport in the Rayleigh-B\'{e} nard
convection problem no-slip boundary conditions for the velocity field are assumed …

This work applies a continuous data assimilation scheme---a framework for reconciling
sparse and potentially noisy observations to a mathematical model---to Rayleigh--Bénard …

This work involves theoretical and numerical analysis of the thermal quasi-geostrophic
(TQG) model of submesoscale geophysical fluid dynamics (GFD). Physically, the TQG model …

This present paper is dedicated to the study of the Cauchy problem of the two-dimensional
Euler-Boussinesq-Bénard equations which couple the incompressible Euler equations for …

The efficiency of a nudging data assimilation algorithm using higher order finite element
interpolating operators is studied. Numerical experiments are presented for the 2D Navier …

We show that small perturbations of the spatially homogeneous equilibrium of a thermally
driven compressible viscous fluid are globally stable. Specifically, any weak solution of the …

We propose and prove several regularity criteria for the 2D and 3D Kuramoto–Sivashinsky
equation, in both its scalar and vector forms. In particular, we examine integrability criteria for …

This article is concerned with the problem of determining an unknown source of non-
potential, external time-dependent perturbations of an incompressible fluid from large-scale …

We propose, analyze, and test a novel continuous data assimilation two-phase flow
algorithm for reservoir simulation. We show that the solutions of the algorithm, constructed …

We consider the physically relevant fully compressible setting of the Rayleigh–Bénard
problem of a fluid confined between two parallel plates, heated from the bottom, and …