Related papers: Large time behavior of solutions to a dissipative …
In this paper, we investigate the long-time behavior of the two-dimensional incompressible Boussinesq system with kinematic viscosity in a periodic channel, focusing on instability and asymptotic stability near hydrostatic equilibria.…
We rigorously justify in 3D the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems, Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre approximation and…
We address the long time behavior of the Boussinesq system coupling the Navier-Stokes equations driven by density with the non-diffusive equation for the density. We construct solutions of the system justifying previously obtained a priori…
In this paper a three-parameter family of Boussinesq systems is studied. The systems have been proposed as models of the propagation of long internal waves along the interface of a two-layer system of fluids with rigid-lid condition for the…
Dissipative wave equations with critical quintic nonlinearity and damping term involving the fractional Laplacian are considered. The additional regularity of energy solutions is established by constructing the new Lyapunov-type functional…
This paper deals with the interactions of waves governed by a non-linear dispersive Boussinesq type system with the vertical displacement of a cylindrical floating structure in an axisymmetric without swirl situation. The Boussinesq regime…
This work is focused on the dissipative system describing the dynamics of an extensible thermoelastic beam, where the dissipation is entirely contributed by the second equation ruling the evolution of the temperature. Under natural boundary…
The existence of a global attractor for the solution semiflow of the extended Brusselator system in the $L^2$ phase space is proved, which is a cubic-autocatalytic and partially reversible reaction-diffusion system with linear coupling…
In this manuscript, we consider the $3$D Boussinesq equations for stably stratified fluids with the horizontal viscosity and thermal diffusivity and investigate the large time behavior of the solutions. Making use of the anisotropic…
In this paper, we review the history and current state-of-the-art in the modelling of long nonlinear dispersive waves. For the sake of conciseness of this review, we omit the unidirectional models and focus especially on some classical and…
A higher-order nonlinear Boussinesq system with a time-dependent boundary delay is considered. Sufficient conditions are presented to ensure the well-posedness of the problem by utilizing Kato's variable norm technique and the Fixed-Point…
This paper establishes the nonlinear stability of the Couette flow for the 2D Boussinesq equations with only vertical dissipation. The Boussinesq equations concerned here model buoyancy-driven fluids such as atmospheric and oceanographic…
Boussinesq systems of nonlinear partial differential equations are fundamental equations in geophysical fluid dynamics. In this paper, we use asymmetric ideas and moving frames to solve the two-dimensional Boussinesq equations with partial…
The paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials, including the possibility of dissipation. The dissipative term chosen is similar to the classical…
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…
The numerical approximation of some Boussinesq systems in two spatial dimensions is here considered. The differential systems under study are proposed as asymptotic models for the propagation of waves along the interface of two layers of…
We regard the Cauchy problem for a particular Whitham-Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. We are interested in well-posedness at a very low level of regularity. We derive dispersive and…
In this study, the numerical analysis of a specific fluid-solid interaction problem is detailed. The weakly nonlinear Boussinesq system is considered with the addition of a solid object lying on the flat bottom, allowed to move horizontally…
We study the two dimensional viscous Boussinesq equations, which model stratified flows in a circular domain under the influence of a general gravitational potential $f$. First, we show that the Boussinesq equations admit steady-state…
In this paper, we consider the viscous, incompressible, nonlinear Boussinesq system in two and three spatial dimension. We study the existence and regularity of solutions to the Boussinesq system with nonhomogeneous boundary conditions for…