Related papers: Long time existence for a class of weakly transver…

We prove a long time existence result for the solutions of a two-dimensional Boussinesq system modeling the propagation of long, weakly nonlinear water waves. This system is exceptional in the sense that it is the only linearly well-posed…

This paper is a continuation of a previous work by two of the Authors on long time existence for Boussinesq systems modeling the propagation of long, weakly nonlinear water waves. We provide proofs on examples not considered previously in…

In this paper we deal with the long time existence for the Cauchy problem associated to some asymptotic models for long wave, small amplitude gravity surface waves. We generalize some of the results that can be found in the literature…

We study the Cauchy problem for one-dimensional dispersive system of Boussinesq type which models weakly nonlinear long wave surface waves. We establish the local well-posedness and ill-posedness of solutions to the system. We also provide…

This paper is concerned with the one-dimensional version of a specific member of the (abcd) family of Boussinesq systems having the higher possible dispersion. We will establish two different long time existence results for the solutions of…

In this paper we deal with the long time existence for the Cauchy problem associated to BBM-type Boussinesq systems of equations which are asymptotic models for long wave, small amplitude gravity surface water waves. As opposed to previous…

Consideration is given to three different full dispersion Boussinesq systems arising as asymptotic models in the bi-directional propagation of weakly nonlinear surface waves in shallow water. We prove that, under a non-cavitation condition…

We prove in this paper a long time existence result for a modified Boussinesq-Peregrine equation in one dimension, describing the motion of Water Waves in shallow water, in the case of a non flat bottom. We first give a local existence…

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…

We prove the long time existence of solutions of a Boussinesq system with strong topography variations.

This paper is concerned with a two dimensional Whitham-Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. We prove that the associated Cauchy problem is well-posed for initial data of low regularity, with…

In this article we consider the Boussinesq system supplemented with some dissipation terms. These equations model the propagation of a waterwave in shallow water. We prove the existence of a global smooth attractor for the corresponding…

We consider in this paper the well-posedness for the Cauchy problem associated to two-dimensional dispersive systems of Boussinesq type which model weakly nonlinear long wave surface waves. We emphasize the case of the {\it strongly…

Considered herein are a number of variants of the Boussinesq type systems modeling surface water waves. Such equations were derived by different authors to describe the two-way propagation of long gravity waves. A question of existence of…

This study deals with higher-ordered asymptotic equations for the water-waves problem. We considered the higher-order/extended Boussinesq equations over a flat bottom topography in the well-known long wave regime. Providing an existence and…

In this note, we prove local-in-time well-posedness for a fully dispersive Boussinesq system arising in the context of free surface water waves in two and three spatial dimensions. Those systems can be seen as a weak nonlocal dispersive…

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…

In this paper, we study the generalized Boussinesq equation as a model for the water wave problem with surface tension. Initially, we investigate the initial value problem within Sobolev spaces, deriving conditions under which solutions are…

In this paper we address the Cauchy problem for two systems modeling the propagation of long gravity waves in a layer of homogeneous, incompressible and inviscid fluid delimited above by a free surface, and below by a non-necessarily flat…

In this paper, we investigate the well-posedness of a nonlinear dispersive model with variable coefficients that describes the evolution of surface waves propagating through a one-dimensional shallow water channel of finite length with…