Abstract Consideration is given to three different full dispersion Boussinesq systems arising as asymptotic models in the bi-directional propagation of weakly nonlinear surface waves shallow water. We prove that, under a non-cavitation condition on initial data, these are well-posed time scale order <mml:math xmlns:mml="http://www.w3.org/1998/Math...

In this paper, we establish the well-posedness for third grade fluid equation perturbed by a multiplicative white noise. This describes motion of non-Newtonian differential type with relevant viscoelastic properties. We are faced strongly nonlinear stochastic partial supplemented Navier slip boundary condition. Taking initial condition in Sobolev space H2, show existence and uniqueness strong (...

We obtain local well-posedness result for the generalized Hall-magneto-hydrodynamics system in Besov spaces $${\dot{B}^{-(2\alpha _1-\gamma )}_{\infty , \infty }} \times {\dot{B}^{-(2\alpha _2-\beta }({{\mathbb {R}}^3})}$$ with suitable indexes $$\alpha _1, \alpha _2, \beta $$ and $$\gamma .$$ As a corollary, hyperdissipative electron magneto-hydrodynamics is globally well-posed _2-2)}}_{\infty...

Uniqueness and continuous dependence of solutions of (2) can thus be derived from the well-posedness of the Cauchy problem for (3). We remark that the genuine nonlinearity of (1) implies that the total variation of u(t0, ·) is locally bounded, for each t0 > 0. Hence the well posedness of the Cauchy problem (3) with initial data x(t0) = x0 follows from [2]. It is worth noting that in [3] the wel...

In this short note, we study the local well-posedness of a 3D model for incompressible Navier-Stokes equations with partical viscosity. This model was originally proposed by Hou-Lei in [4]. In a recent paper, we prove that this 3D model with partial viscosity will develop a finite time singularity for a class of initial condition using a mixed Dirichlet Robin boundary condition. The local well-...

We consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi 1995, 1996 for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the class of mixed variational inequalities. We establish some metric characterizations of the well-posedness by perturbations. On the other hand, it is ...

In the present paper, we generalize the concept of well-posedness to a generalized hemivariational inequality, give some metric characterizations of the α-well-posed generalized hemivariational inequality, and derive some conditions under which the generalized hemivariational inequality is strongly α-well-posed in the generalized sense. Also, we show that the α-well-posedness of the generalized...

We study dispersive models of fluid flow in viscoelastic vessels, derived the blood flow. The unknowns are velocity axial direction and displacement vessel wall from rest. prove that one such model has a well-posed initial value problem, while we argue related instead an ill-posed problem; second case, still existence solutions analytic function spaces. Finally some periodic traveling waves.

The purpose of this paper is to investigate the problems of the well-posedness for a system of mixed quasivariational-like inequalities in Banach spaces. First, we generalize the concept of α-well-posedness to the system of mixed quasivariational-like inequalities, which includes symmetric quasi-equilibrium problems as a special case. Second, we establish some metric characterizations of α-well...