相关论文: Oscillatory convection and limitations of the Bous…
We consider a class of Boussinesq systems of Bona-Smith type in two space dimensions approximating surface wave flows modelled by the three-dimensional Euler equations. We show that various initial-boundary-value problems for these systems,…
This study considers the onset of stress-free Boussinesq thermal convection in rotating spherical shells with aspect ratio $\eta=r_i/r_o=0.9$ ($r_i$ and $r_o$ being the inner and outer radius), Prandtl numbers ${\rm Pr}…
We investigate the asymptotic stability of solution to Boussinesq equations without thermal conduction with the initial data near a specific stationary solution in the three--dimensional domain $\Omega = \mathbb{R}^{2}\times (0,1)$. It is…
In this work we study the validity of the rotating wave approximation of an ideal system composed of two harmonic oscillators evolving with a quadratic Hamiltonian and arbitrarily strong interaction. We prove its validity for arbitrary…
We consider a general compressible viscous and heat conducting fluid confined between two parallel plates and heated from the bottom. The time evolution of the fluid is described by the Navier--Stokes--Fourier system considered in the…
Buoyancy-induced (Rayleigh-Benard) convection of a fluid between two horizontal plates is a central paradigm for studying the transition to complex spatiotemporal dynamics in sustained nonequilibrium systems. To improve the analysis of…
In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…
An asymptotic expansions for the grand partition function of ideal Bose gas in the canonical ensemble with arbitrary number of particles is obtained. It is shown that the expressions found are valid in the whole temperature region, the…
We consider the Oberbeck--Boussinesq approximation driven by an inhomogeneous temperature distribution on the boundary of a bounded fluid domain. The relevant boundary conditions are perturbed by a non--local term arising in the…
Convection in the Sun occurs at Rayleigh numbers, $Ra$, as high as $10^{22}$, molecular Prandtl numbers, $Pr$, as low as $10^{-6}$, under conditions that are far from satisfying the Oberbeck-Boussinesq (OB) idealization. The effects of…
The Boussinesq $abcd$ system is a 4-parameter set of equations posed in $\mathbb{R}_t \times \mathbb{R}_x$, originally derived by Bona, Chen and Saut as first order 2-wave approximations of the incompressible and irrotational, two…
This paper presents a theory describing the energy budget of a fluid under the Boussinesq approximation: the theory is developed in a manner consistent with the conservation law of mass. It shows that no potential energy is available under…
We study the three-dimensional, incompressible, non-hydrostatic Boussinesq fluid equations, which are applicable to the dynamics of the oceans and atmosphere. These equations describe the interplay between velocity and buoyancy in a…
We consider the 2D Boussinesq equations with a velocity damping term in a strip $\mathbb{T}\times[-1,1]$, with impermeable walls. In this physical scenario, where the \textit{Boussinesq approximation} is accurate when density/temperature…
The Bousso entropy bound, in its generalized form, is investigated for the case of perfect fluids at local thermodynamic equilibrium and evidence is found that the bound is satisfied if and only if a certain local thermodynamic property…
We examine non-singular bounce cosmology within the framework of a phantom scalar field coupled to the Gauss-Bonnet term in both non-viscous and bulk-viscous cases. Using the scale factor ansatz…
In this paper, we deal with the global exact controllability to the trajectories of the Boussinesq system. We consider 2D and 3D smooth bounded domains. The velocity field of the fluid must satisfy a Navier slip-with-friction boundary…
In this paper, we improve the global existence result in [9] slightly. More precisely, the global existence of strong solutions to the primitive equations with only horizontal viscosity and diffusivity is obtained under the assumption of…
Large-scale patterns, which are well-known from the spiral defect chaos regime of thermal convection at Rayleigh numbers $Ra < 10^4$, continue to exist in three-dimensional numerical simulations of turbulent Rayleigh-B\'{e}nard convection…
We study the behaviour of an ideal non-relativistic Bose gas in a three-dimensional space where one of the dimensions is compactified to form a circle. In this case there is no phase transition like that for the case of an infinite volume,…