A possible counterexample to well posedness of entropy solutions and to Godunov scheme convergence

A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they suggest that entropy solutions (in the weak entropy inequality sense) are not well posed.

     

Reference values for drag and lift of a two‐dimensional time‐dependent flow around a cylinder

This paper presents a numerical study of a two‐dimensional time‐dependent flow around a cylinder. Its main objective is to provide accurate reference values for the maximal drag and lift coefficient at the cylinder and for the pressure difference between the front and the back of the cylinder at the final time. In addition, the accuracy of these values obtained with different time stepping schemes and different finite element methods is studied. Copyright © 2004 John Wiley & Sons, Ltd.     

Mesophase behaviour of 2,5-dibenzoyloxy-p-benzoquinone derivatives and tetrahydrobenzene tetraesters

The synthesis of 2,5-dibenzoyloxy-p-benzoquinone derivatives, their products after reduction and tetraesters from tetrahydroxybenzene prepared from those products is described. Their phase behaviour was investigated by differential scanning calorimetry and polarizing microscopy and is discussed in terms of their detailed structure.     

Local solution for the Kadomtsev-Petviashvili equation with periodic conditions

In this article we prove a local existence and uniqueness theorem for the Kadomtsev-Petviashvili Equation (u _t +u _xxx +uu _x ) _x −u _yy =0) in the Sobolev spaces of orders≥3, with initial values in the same spaces, and periodic boundary conditions. This theorem improves previous results based upon the application of singular perturbation techniques.     

Rigidity in holomorphic and quasiregular dynamics

We consider rigidity phenomena for holomorphic functions and then more generally for uniformly quasiregular maps.