Nonlinear Instability for Nonhomogeneous Incompressible Viscous Fluids

We investigate the nonlinear instability of a smooth steady density profile solution of the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field, including a Rayleigh-Taylor steady-state solution with heavier density with increasing height (referred to the Rayleigh-Taylor instability). We first analyze the equations obtained from linearization around the steady density profile solution. Then we construct solutions of the linearized problem that grow in time in the Sobolev space Hk, thus leading to a global instability result for the linearized problem. With the help of the constructed unstable solutions and an existence theorem of classical solutions to the original nonlinear equations, we can then demonstrate the instability of the nonlinear problem in some sense. Our analysis shows that the third component of the velocity already induces the instability, this is different from the previous known results.Comment: 24 page

An overview of arisings and large-scale treatment technologies for healthcare waste in the United Kingdom

This paper reviews the current generation and management of healthcare waste in the United Kingdom, with a focus on that produced from healthcare provision in the National Health Service. While the current capacities of large-scale off-site treatment systems are adequate, there are a number of logistical factors that must be considered in future. These include variations in arisings from each country and from various regions within each country, the age and location of treatment/disposal facilities, the quantities, types and sources of healthcare waste, and the impact of waste minimization and recycling strategies. Managing UK healthcare waste is a complex issue that requires the correct technologies and capacities to be available. With increasing quantities and costs there is urgent need for future planning, and healthcare waste issues need to be addressed from a UK-wide perspective. Holistic strategies need to incorporate both minimization and segregation, with treatment using a combination of incineration and alternatives treatment technologies. The need for more research and accurate data to provide an evidence base for future decision making is high lighte