The weak sigma-attractor for the semi-dissipative 2D Boussinesq system

Stochastic Weak Attractor for a Dissipative Euler

The global attractor of the 2D Boussinesq system with fractional vertical dissipation

The 2D incompressible Boussinesq system with partial or fractional dissipation have recently attracted considerable attention. In this paper, we study the Cauchy problem for the 2D Boussinesq system in a periodic domain with fractional vertical dissipation in the subcritical case, and we prove the global well-posedness of strong solutions. Based on this, we also discuss the existence of the glo...

Dissipative Boussinesq system of equations in the Bénard-Marangoni phenomenon.

By using the long-wave approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a BénardMarangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it can be interpreted as a dissipative generalization of the usual Boussinesq system of equations. As a particular case, a strictly dissipative version of the Boussines...

Dissipative Boussinesq equations

The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated nu...

Exponential Attractor for a First-Order Dissipative Lattice Dynamical System

Lattice systems arise in many applications, for example, in chemical reaction theory, image processing, pattern recognition, material science, biology, electrical engineering, laser systems, and so forth. A lattice dynamical system LDS is an infinite system of ordinary differential equations lattice ODEs or of difference equations. In some cases, they arise from spatial discretizations of parti...