We present a mathematical description of wetting and drying stone pores, where the resulting mathematical model contains hysteresis operators. We describe these hysteresis operators and present a numerical solution for a simplified problem.
The shape and velocity of a sliding droplet are computed by solving the Navier-Stokes equation with free interface boundary conditions. The Galerkin finite element method is implemented in a 2D computation domain discretized using an unstructured mesh with triangular elements. The mesh is refined recursively at the corners (contact points). The stationary sliding velocity is found to be strongly dependent on grid refinement, which is a consequence of the contact line singularity resolved through...
We study the stability of self-similar solutions of the binormal flow, which is a model for the dynamics of vortex filaments in fluids and super-fluids. These particular solutions form a family of evolving regular curves in that develop a singularity in finite time, indexed by a parameter . We consider curves that are small regular perturbations of for a fixed time . In particular, their curvature is not vanishing at infinity, so we are not in the context of known results of local existence...
We study the decay in time of solutions of a symmetric regularized-long-wave equation and we show that under some restriction on the form of nonlinearity, the solutions of the nonlinear equation have the same long time behavior as those of the linear equation. This behavior allows us to establish a nonlinear scattering result for small perturbations.
We discuss new MUSCL reconstructions to approximate the solutions of hyperbolic systems of conservations laws on 2D unstructured meshes. To address such an issue, we write two MUSCL schemes on two overlapping meshes. A gradient reconstruction procedure is next defined by involving both approximations coming from each MUSCL scheme. This process increases the number of numerical unknowns, but it allows to reconstruct very accurate gradients. Moreover a particular attention is paid on the limitation...
In this paper sufficient optimality conditions are established for optimal control of both steady-state and instationary Navier-Stokes equations. The second-order condition requires coercivity of the Lagrange function on a suitable subspace together with first-order necessary conditions. It ensures local optimality of a reference function in a -neighborhood, whereby the underlying analysis allows to use weaker norms than .
In this paper sufficient optimality conditions are established for optimal control of both steady-state and instationary Navier-Stokes equations. The second-order condition requires coercivity of the Lagrange function on a suitable subspace together with first-order necessary conditions. It ensures local optimality of a reference function in a Ls-neighborhood, whereby the underlying analysis allows to use weaker norms than L∞.
Blood rheology is completely determined by its major corpuscles which are erythrocytes, or red blood cells (RBCs). That is why understanding and correct mathematical description of RBCs behavior in blood is a critical step in modelling the blood dynamics. Various phenomena provided by RBCs such as aggregation, deformation, shear-induced diffusion and non-uniform radial distribution affect the passage of blood through the vessels. Hence, they have...
The most important result stated in this paper is a theorem on the existence of global solutions for the Navier-Stokes equations in Rn when the initial velocity belongs to the space weak Ln(Rn) with a sufficiently small norm. Furthermore, this fact leads us to obtain self-similar solutions if the initial velocity is, besides, an homogeneous function of degree -1. Partial uniqueness is also discussed.
In this paper, we study the semiclassical limit of the cubic nonlinear Schrödinger equation with the Neumann boundary condition in an exterior domain. We prove that before the formation of singularities in the limit system, the quantum density and the quantum momentum converge to the unique solution of the compressible Euler equation with the slip boundary condition as the scaling parameter approaches
We consider the Cauchy problem for the three-dimensional Navier-Stokes equations, and provide an optimal regularity criterion in terms of and , which are the third components of the velocity and vorticity, respectively. This gives an affirmative answer to an open problem in the paper by P. Penel, M. Pokorný (2004).