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We analyze the equation coming from the Eulerian–Lagrangian description of fluids. We discuss a couple of ways to extend this notion to viscous fluids. The main focus of this paper is to discuss the first way, due to Constantin. We show that this description can only work for short times, after which the " back to coordinates map " may have no smooth… (More)
A graph is integral if all the eigenvalues of its adjacency matrix are integers. In this paper we give sufficient conditions for complete 3-partite graphs to be integral, from which we construct infinitely many new classes of such integral graphs.
We study axisymmetric solutions to the Navier-Stokes equations in the whole three-dimensional space. We find conditions on the radial and angular components of the velocity field which are sufficient for proving the regularity of weak solutions.
We study the non-stationary Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axisymmetric. We extend the regularity criterion for axisymmetric weak solutions given in .
We study the motion of the steady compressible heat conducting viscous fluid in a bounded three dimensional domain governed by the compressible Navier-Stokes-Fourier system. Our main result is the existence of a weak solution to these equations for arbitrarily large data. A key element of the proof is a special approximation of the original system… (More)
The paper summarizes the experience with the dilatation of malignant oesophageal stenosis by a balloon catheter. In a patient after gastrectomy with a relapse of the tumorous process the author performed 10 dilatation interventions by a balloon 22 mm wide. After a short interval of renewed normal passage, marked swallowing difficulties always rapidly… (More)
The dilatation of oesophagus oral portion in the Kelly-Paterson (Plummer Vinson) syndrome was made in two female patients at the age of 58 and 81 years. For the extreme stenosis (2 and 3 mm) of the lumen the dilatation was first performed by the Grüntzig Catheter and after extension above 5 mm special oesophageal catheters with a balloon of 15 mm diameter… (More)
We present a complete existence theory for the physical system consisting of a viscous com-pressible fluid and a number of rigid bodies in it. We assume a bounded domain and homogeneous Dirichlet boundary conditions for the velocity. Both the fluid and the bodies are allowed to be heat-conducting and share the heat. The existence of global-in-time… (More)