New exact solutions are obtained for several nonlinear physical equations, namely the Navier–Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinear Schrödinger equation. The solution methods make use of the symmetry group of the system in situations when the standard Lie method of symmetry reduction is not applicable.

A simple model is presented for the time-averaged electron mobility within a Hall thruster. The model is predicated on the experimental evidence for isentropic electron flow and, when used in a one-dimensional simulation, captures plasma properties that are in reasonable agreement with experiment.

We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a strong solution so that it is unique in a class of weak solutions. Known weak-strong uniqueness results are improved. Classical uniqueness results for this equation follow naturally.

Abstract: We prove the existence of global weak solutions to the Navier-Stokes equations for compressible isentropic fluids for any γ > 1 when the Cauchy data are helically symmetric, where the constant γ is the specific heat ratio. Moreover, a new integrability estimate of the density in any neighborhood of the symmetry axis (the singularity axis) is obtained.

In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for two-dimensional flow of Chaplygin gases.

We consider a semidiscrete kinetic scheme for the isentropic gas dynamic system with γ = 3 which corresponds exactly to the “transport-collapse method” of Brenier. We show the existence of shock profiles for every admissible limit values. In addition we give properties of such profiles.

In this paper we focus on the initial-boundary value problem of the 2-D isentropic Euler equations with damping. We prove the global-intime existence of classical solution to the initial-boundary value problem by the method of energy estimates. keywords: Euler equation; initial-boundary value problem; well-posedness. MSC(2000): 35A05; 35L45.

The direct inversion method for data assimilation using isentropic tracer advection M. N. Juckes British Atmospheric Data Centre, SSTD, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, UK Received: 15 June 2005 – Accepted: 13 July 2005 – Published: 19 September 2005 Correspondence to: M. Juckes ([email protected]) © 2005 Author(s). This work is licensed under a Creative...

The main purpose of this paper is to analyze the sensitivity of system parameters to the performance of the Organic Rankine Cycle (ORC) system quantitatively. A thermodynamic model of the ORC system for binary-cycle geothermal power plants has been developed and verified. The system parameters, such as working fluid, superheat temperature, pinch temperature difference in evaporator and condense...

In this paper performance characteristics for a Ranque-Hilsch vortex tube are presented. The was of divergent design and optimised both size performance, to be used supply cold air turbomachinery experiments with feed in the pressure range 3.0–7.0 bar, overall mass flow rates 0.05–0.14 kg/s. Optimum fixed parameters selected from literature were: ratio cold-exit diameter inlet internal (0.50); ...