In this paper we are concerned with the steady Boussinesq system with mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak, one-sided leak, velocity, vorticity, pressure and stress conditions together and the conditions for temperature may include Dirichlet, Neumann and Robin conditions together. For the problem involving the static pressure and stress boundary conditions, it is proved that if the data of the problem are small enough, then there exists a solution...

We consider the steady plane flow of certain classes of viscoelastic fluids in exterior domains with a non-zero velocity prescribed at infinity. We study existence as well as asymptotic behaviour of solutions near infinity and show that for sufficiently small data the solution decays near infinity as fast as the fundamental solution to the Oseen problem.

In this paper, the axisymmetric flow in an ideal fluid outside the infinite cylinder ($r\le d$) where $(r,\theta ,z)$ denotes the cylindrical co-ordinates in ${ℝ}^3$ is considered. The motion is with swirl (i.e. the $\theta$-component of the velocity of the flow is non constant). The (non-dimensional) equation governing the phenomenon is (Pd) displayed below. It is known from e.g. that for the problem without swirl ($f_q=0$ in (f)) in the whole space, as the flux constant $k$ tends to $\infty$, 1) $\mathrm{dist}(0z,\partial A)=O\left(k^{1/2}\right)$; $\mathrm{diam}A=O(exp(-c_0{k}^{3/2}))$; 2) ${\left(k^{1/2}\Psi \right)}_{k\in \mathbb{N}}$ converges to a vortex cylinder $U_m$ (see...

Steady-state system of equations for incompressible, possibly non-Newtonean of the $p$-power type, viscous flow coupled with the heat equation is considered in a smooth bounded domain $\Omega \subset {ℝ}^n$, $n=2$ or 3, with heat sources allowed to have a natural $L^1$-structure and even to be measures. The existence of a distributional solution is shown by a fixed-point technique for sufficiently small data if $p>3/2$ (for $n=2$) or if $p>9/5$ (for $n=3$).

In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system with surface tension. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to construct the solutions in [3]. On the other hand, for smoother initial data, we prove that the solutions enjoy the optimal Strichartz estimates (i.e, without loss of regularity compared to the system linearized at ($\eta =0,\psi =0$)).

We classify in this article the structure and its transitions/evolution of the Taylor vortices with perturbations in one of the following categories: a) the Hamiltonian vector fields, b) the divergence-free vector fields, and c). the solutions of the Navier-Stokes equations on the two-dimensional torus. This is part of a project oriented toward to developing a geometric theory of incompressible fluid flows in the physical spaces.

In this paper, we are interested in modelling the flow of the coolant (water) in a nuclear reactor core. To this end, we use a monodimensional low Mach number model supplemented with the stiffened gas law. We take into account potential phase transitions by a single equation of state which describes both pure and mixture phases. In some particular cases, we give analytical steady and/or unsteady solutions which provide qualitative information about the flow. In the second part of the paper, we introduce...

In this paper, we propose a new diffuse interface model for the study of three immiscible component incompressible viscous flows. The model is based on the Cahn-Hilliard free energy approach. The originality of our study lies in particular in the choice of the bulk free energy. We show that one must take care of this choice in order for the model to give physically relevant results. More precisely, we give conditions for the model to be well-posed and to satisfy algebraically and dynamically consistency...

Three-dimensional anisotropic magneto-hydrodynamical system is investigated in the whole space ${ℝ}^3$. Existence and uniqueness results are proved in the anisotropic Sobolev space $H^{0,s}$ for $s\>1/2$. Asymptotic behavior of the solution when the Rossby number goes to zero is studied. The proofs, where the incompressibility condition is crucial, use the energy method, an appropriate dyadic decomposition of the frequency space, product laws in anisotropic Sobolev spaces and Strichartz-type estimates.