Related papers: Stability and bifurcation of 2D viscous primitive …
We study linear stability of exponential periodic solutions of a system of singular amplitude equations associated with convective Turing bifurcation in the presence of conservation laws, as arises in modern biomorphology models, binary…
A sequence of three steady - oscillatory transitions of buoyancy convection of air in a laterally heated cube with perfectly thermally insulated horizontal and spanwise boundaries is studied. The problem is treated by Newton and Arnoldi…
We analyze the stability and dynamics of bistable planar fronts in multicomponent reaction-diffusion systems on $\mathbb{R}^{d}$. Under standard spectral stability assumptions, we establish Lyapunov stability of the front against fully…
Double-diffusive convection driven by both thermal and compositional buoyancy in a rotating spherical shell can exhibit a rather large number of behaviours often distinct from that of the single diffusive system. In order to understand how…
Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully…
We study the convective patterns that arise in a nearly semi-cylindrical cavity fed in with hot fluid at the upper boundary, bounded by a cold, porous semi-circular boundary at the bottom, and infinitely extended in the third direction.…
We study the steady states and dynamics of a thin film-type equation with non-conserved mass in one dimension. The evolution equation is a nonlinear fourth-order degenerate parabolic PDE motivated by a model of volatile viscous fluid films…
In this paper, we study the long-time behavior of the solutions to the two-dimensional incompressible free Navier Stokes equation (without forcing) with small viscosity $\nu$, when the initial data is close to stable monotone shear flows.…
In this paper, we consider the 3D primitive equations of oceanic and atmospheric dynamics with only horizontal eddy viscosities in the horizontal momentum equations and only vertical diffusivity in the temperature equation. Global…
Consider at a finite temperature $T$ a superfluid moving with a velocity $v$ relative to the thermal bath or its normal component. From Landau's argument there exists a critical $v_c (T)$ beyond which excitations can be spontaneously…
This article investigates the linear stability of thermal-bioconvection within a suspension containing phototactic microorganisms heated from below. In suspension, the upper surface is taken as stress-free, while the lower surface is taken…
This paper investigates the nonlinear stability of Taylor-Couette (TC) flows incorporating the thermal buoyancy within an annular domain characterized by small viscosity $\nu$ and thermal diffusivity $\mu$. It is well established that the…
We consider two-dimensional flows above topography, revisiting the selective decay (or minimum-enstrophy) hypothesis of Bretherton and Haidvogel. We derive a 'condensed branch' of solutions to the variational problem where a domain-scale…
A bidisperse porous medium is one with two porosity scales. There are the usual pores known as macro pores but also cracks or fissures in the skeleton which give rise to micro pores. In this article we develop and analyse a model for…
In order to understand the nonlinear stability of many types of time-periodic travelling waves on unbounded domains, one must overcome two main difficulties: the presence of embedded neutral eigenvalues and the time-dependence of the…
The stability of buoyant flows occurring in the mixed convection regime for a viscous fluid in a horizontal plane-parallel channel with adiabatic walls is investigated. The basic flow features a parallel velocity field under stationary…
The study and characterization of the diversity of spatiotemporal patterns generated when a rectangular layer of fluid is locally heated beneath its free surface is presented. We focus on the instability of a stationary cellular pattern of…
This paper provides the phase transition analysis of a reaction diffusion equations system modeling dynamic instability of microtubules. For this purpose we have generalized the macroscopic model studied by Mour\~ao et all [MSS]. This model…
A water-filled differentially heated rotating annulus with initially prepared stable vertical salinity profiles is studied in the laboratory. Based on two-dimensional horizontal particle image velocimetry (PIV) data, and infrared camera…
Critical dynamics of an ultracold Bose gas far from equilibrium is studied in two spatial dimensions. Superfluid turbulence is created by quenching the equilibrium state close to zero temperature. Instead of immediately re-thermalizing, the…