相关论文: Mechanical balance laws for two-dimensional Boussi…
The Oberbeck-Boussinesq approximation is the most widely employed theoretical scheme for the study of natural or mixed convection flows. However, the misunderstanding of this approximated framework is a possibility that may cause the…
We study here some asymptotic models for the propagation of internal and surface waves in a two-fluid system. We focus on the so-called long wave regime for one dimensional waves, and consider the case of a flat bottom. Starting from the…
We rigorously establish that, in the long-wave regime characterized by the assumptions of long wavelength and small amplitude, bidirectional solutions of the improved Boussinesq equation tend to associated solutions of two uncoupled…
A complete classification of all low-order conservation laws is carried out for a system of coupled semilinear wave equations which is a natural two-component generalization of the nonlinear Klein-Gordon equation. The conserved quantities…
In the work it has been shown that there are two types of the conservation laws. 1. The conservation laws that can be called exact ones. They point to an avalability of some conservative quantities or objects. Such objects are the physical…
In this paper, we consider the Boussinesq equations with magnetohydrodynamics convection in the domain $\mathbb{T} \times \mathbb{R}$ and establishes the nonlinear stability of the Couette flow $(\mathbf{u}_{sh} = (y,0), \mathbf{b}_{sh} =…
We address justification and solitary wave solutions of the cylindrical KdV equation which is formally derived as a long wave approximation of radially symmetric waves in a two-dimensional nonlinear dispersive system. For a regularized…
We address the long-time behavior of the 2D Boussinesq system, which consists of the incompressible Navier-Stokes equations driven by a non-diffusive density. We construct globally persistent solutions on a smooth bounded domain, when the…
In the works by the author it has been shown that the conservation laws for material media (the conservation laws for energy, linear momentum, angular momentum, and mass, that establish a balance between the variation of a physical quantity…
We show that the semi-implicit time discretization approaches previously introduced for multilayer shallow water models for the barotropic case can be also applied to the variable density case with Boussinesq approximation. Furthermore,…
We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…
This article deals with relaxation approximations of nonlinear systems of hyperbolic balance laws. We introduce a class of relaxation schemes and establish their stability and convergence to the solution of hyperbolic balance laws before…
We construct a special asymptotic solution for the forced Boussinesq equation. The perturbation is small and oscillates with a slowly varied frequency. The slow passage through the resonance generates waves with the finite amplitude. This…
The goal of this work is to study waves interacting with partially immersed objects allowed to move freely in the vertical direction, and in a regime in which the propagation of the waves is described by the one dimensional…
Dipole-conserving fluids serve as examples of kinematically constrained systems that can be understood on the basis of symmetry. They are known to display various exotic features including glassylike dynamics, subdiffusive transport, and…
We consider the evolution of two incompressible fluids with homogeneous densities $\rho_-<\rho_+$ subject to gravity described by the inviscid Boussinesq equations and provide the explicit relaxation of the associated differential…
We present some recent developments on shock capturing methods for nonlinear hyperbolic systems of balance laws, whose prototype is the Euler system of compressible fluid flows, and especially discuss {structure-preserving} techniques. The…
We establish the long time existence of solutions for the "Boussinesq-Full Dispersion" systems modeling the propagation of internal waves in a two-layer system. For the two-dimensional Hamiltonian case we prove the global existence of small…
The general equations of motion for ocean dynamics are presented and the waves supported by the (inviscid, unforced) linearized system with respect to a state of rest are derived. The linearized dynamics sustains one zero frequency mode…
We study the behavior of shallow water waves propagating over bathymetry that varies periodically in one direction and is constant in the other. Plane waves traveling along the constant direction are known to evolve into solitary waves, due…