Viene provata l'esistenza e l'unicità delle soluzioni deboli per un sistema di equazioni della magnetoidrodinamica in un dominio variabile. Per la dimostrazione si usano il metodo di Galerkin spettrale e la tecnica introdotta da Dal Passo e Ughi per trattare i problemi con dominio dipendente dal tempo.

We consider a body immersed in a perfect gas and moving under the action of a constant force. Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body, it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction. We study the approach of the body velocity V(t) to the limiting velocity $V_{\infty }$ and prove that, under suitable smallness assumptions, the approach...

We study the flat region of stationary points of the functional ${\int }_{\Omega }F\left(\right|\nabla u\left(x\right)\left|\right)dx$ under the constraint $u\le M$, where $\Omega$ is a bounded domain in ${ℝ}^2$. Here $F\left(s\right)$ is a function which is concave for $s$ small and convex for $s$ large, and $M>0$ is a given constant. The problem generalizes the classical minimal resistance body problems considered by Newton. We construct a family of partially flat radial solutions to the associated stationary problem when $\Omega$ is a ball. We also analyze some other qualitative properties. Moreover, we show the...

We study the pathwise regularity of the map φ↦I(φ)=∫0T〈φ(Xt), dXt〉, where φ is a vector function on ℝd belonging to some Banach space V, X is a stochastic process and the integral is some version of a stochastic integral defined via regularization. A continuous version of this map, seen as a random element of the topological dual of V will be called stochastic current. We give sufficient conditions for the current to live in some Sobolev space of distributions and we provide elements to conjecture...

We deal with the numerical simulation of a motion of viscous compressible fluids. We discretize the governing Navier–Stokes equations by the backward difference formula – discontinuous Galerkin finite element (BDF-DGFE) method, which exhibits a sufficiently stable, efficient and accurate numerical scheme. The BDF-DGFE method requires a solution of one linear algebra system at each time step. In this paper, we deal with these linear algebra systems with the aid of an iterative solver. We discuss...

We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with ${\displaystyle \gamma =c_p/c_v=2}$. These equations also modelize the shallow water problem in height-flow rate formulation used to solve the flow in lakes and perfectly well-mixed sea. We establish a convergence result for the time-discretized problem when the momentum equation and the continuity equation are solved with the Galerkin method, without adding a penalization term in the continuity equation as it is made in...

We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with ${\displaystyle \gamma =c_p/c_v=2}$. These equations also modelize the shallow water problem in height-flow rate formulation used to solve the flow in lakes and perfectly well-mixed sea. We establish a convergence result for the time-discretized problem when the momentum equation and the continuity equation are solved with the Galerkin method, without adding a penalization term in the continuity equation as it is made in Lions...

This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to introduce a general concept of well-balancing for numerical schemes solving this kind of systems. Once this concept stated, we investigate the well-balance properties of numerical schemes based on the generalized Roe linearizations introduced by [Toumi, J. Comp. Phys. 102 (1992) 360–373]. Next, this general theory is applied to obtain well-balanced...

This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to introduce a general concept of well-balancing for numerical schemes solving this kind of systems. Once this concept stated, we investigate the well-balance properties of numerical schemes based on the generalized Roe linearizations introduced by [Toumi, J. Comp. Phys.102 (1992) 360–373]. Next, this general theory is applied to obtain well-balanced...

We present a numerical simulation of two coupled Navier-Stokes flows, using ope-rator-split-ting and optimization-based non-overlapping domain decomposition methods. The model problem consists of two Navier-Stokes fluids coupled, through a common interface, by a nonlinear transmission condition. Numerical experiments are carried out with two coupled fluids; one with an initial linear profile and the other in rest. As expected, the transmission condition generates a recirculation within the fluid...

The one-dimensional steady-state convection-diffusion problem for the unknown temperature $y\left(x\right)$ of a medium entering the interval $(a,b)$ with the temperature $y_{min}$ and flowing with a positive velocity $v\left(x\right)$ is studied. The medium is being heated with an intensity corresponding to $y_{max}-y\left(x\right)$ for a constant $y_{max}>y_{min}$. We are looking for a velocity $v\left(x\right)$ with a given average such that the outflow temperature $y\left(b\right)$ is maximal and discuss the influence of the boundary condition at the point $b$ on the “maximizing” function $v\left(x\right)$.