Global Existence for the Generalized Two-Component Hunter–Saxton System

Wave-Breaking and Global Existence for a Generalized Two-Component Camassa-Holm System

In this paper we study a generalized two-component Camassa-Holm system which can be derived from the theory of shallow water waves moving over a linear shear flow. This new system also generalizes a class of dispersive waves in cylindrical compressible hyperelastic rods. We show that this new system can still exhibit the wave-breaking phenomenon. We also determine the exact blow-up rate of such...

Stability of Solitary Waves and Global Existence of a Generalized Two-Component Camassa–Holm System

Global Existence Result for the Generalized Peterlin Viscoelastic Model

We consider a class of differential models of viscoelastic fluids with diffusive stress. These constitutive models are motivated by Peterlin dumbbell theories with a nonlinear spring law for an infinitely extensible spring. A diffusion term is included in the constitutive model. Under appropriate assumptions on the nonlinear constitutive functions, we prove global existence of weak solutions fo...

Some existence results for generalized vector quasi-equilibrium problems

‎In this paper‎, ‎we introduce and study a class of generalized vector quasi-equilibrium problem‎, ‎which includes many vector equilibrium problems‎, ‎equilibrium problems‎, ‎vector variational inequalities and variational inequalities as special cases‎. ‎Using one person game theorems‎, ‎the concept of escaping sequences and without convexity assumptions‎, ‎we prove some existence results for ...

Global Existence Results for the Anisotropic Boussinesq System in Dimension Two

We study the global existence issue for the two-dimensional Boussinesq system with horizontal viscosity in only one equation. We first examine the case where the Navier-Stokes equation with no vertical viscosity is coupled with a transport equation. Second, we consider a coupling between the classical two-dimensional incompressible Euler equation and a transportdiffusion equation with diffusion...