Related papers: Long time existence for a two-dimensional strongly…
We apply a multiple-time version of the reductive perturbation method to study long waves as governed by the Boussinesq model equation. By requiring the absence of secular producing terms in each order of the perturbative scheme, we show…
We study the Abels-Garcke-Gr\"un (AGG) model for a mixture of two viscous incompressible fluids with different densities. The AGG model consists of a Navier-Stokes-Cahn-Hilliard system characterized by a (non-constant)…
The $L^2$--gradient flow of the elastic energy of networks leads to a Willmore type evolution law with nontrivial nonlinear boundary conditions. We show local in time existence and uniqueness for this elastic flow of networks in a Sobolev…
We study in this article the blow-up of solutions to a coupled semilinear wave equations which are characterized by linear damping terms in the \textit{scale-invariant regime}, time-derivative nonlinearities, mass terms and Tricomi terms.…
The Cauchy problem of a multi-dimensional ($d\geqslant 2$) compressible viscous liquid-gas two-phase flow model is concerned in this paper. We investigate the global existence and uniqueness of the strong solution for the initial data close…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…
The aim of this article is to prove new ill-posedness results concerning the nonlinear "good" Boussinesq equation, for both the periodic and non-periodic initial value problems. Specifically, we prove that the associated flow map is not…
This paper aims to establish the global well-posedness of the Euler-Poisson system for ions in 2D. The difficulties arising from time resonance at low frequencies and slow decay will be overcome by applying the method developed for the…
We present the recent result [8] concerning the existence of quasi-periodic in time traveling waves for the 2d pure gravity water waves system in infinite depth. We provide the first existence result of quasi-periodic water waves solutions…
In this paper we prove the existence and regularity of a solution to a two-dimensional system of evolutionary hemivariational inequalities which describes the Boussinesq model with nonmonotone friction and heat flux. We use the time…
This paper is devoted to the modeling of longitudinal strain waves in a rod composed of a nonlinear viscoelastic material characterized by frequency-dependent second- and third-order elastic constants. We demonstrate that long waves in such…
We study the waves at the interface between two thin horizontal layers of immiscible liquids subject to high-frequency tangential vibrations. Nonlinear governing equations are derived for the cases of two- and three-dimensional flows and…
In this paper, we investigate a system coupled by nonhomogeneous incompressible Navier-Stokes equations and Allen-Cahn equations describing a diffuse interface for two-phase flow of viscous fluids with different densities in a bounded…
The classical system of shallow-water (Saint--Venant) equations describes long surface waves in an inviscid incompressible fluid of a variable depth. Although shock waves are expected in this quasilinear hyperbolic system for a wide class…
We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…
The linear wave and geostrophic (vortex) solutions are shown to be a complete basis for physical variables $(u,v,w,\rho)$ in a rotating non-hydrostatic Boussinesq model with arbitrary stratification. As a consequence, the fluid can be…
We consider a flow of non-Newtonian incompressible heat conducting fluids with dissipative heating. Such system can be obtained by scaling the classical Navier--Stokes--Fourier problem. As one possible singular limit may be obtained the…
We prove the existence of a weak solution to a two-dimensional resonant 3x3 system of conservation laws with BV initial data. Due to possible resonance (coinciding eigenvalues), spatial BV estimates are in general not available. Instead, we…
We study here Green-Naghdi type equations (also called fully nonlinear Boussinesq, or Serre equations) modeling the propagation of large amplitude waves in shallow water. The novelty here is that we allow for a general vorticity, hereby…
The evolution of two partially miscible, nonhomogeneous, incompressible viscous fluids of non-Newtonian type, can be governed by the Navier-Stokes-Cahn-Hilliard system. In the present work, we prove the global existence of weak solutions…