Some Mathematical Theories of the 'Ghost-effect' in the Boltzmann Equation

Description

The fundamental equation in statistical physics for rarefied gases is the celebrated Boltzmann equation, which gives a description of the time evolution of the particle distribution. Despite its close relation to the classical systems in fluid dynamics, it provides more information at the microscopic level, so that it describes some phenomena which can not be modelled by using the classical systems of Euler and Navier-Stokes equations. The mathematical formulation and numerical computation on the basis of kinetic equations have been studied since the 1960s. This type of phenomena is called the "ghost effect", which is the main topic in this research proposal. Based on previous studies of the Boltzmann equation, in this research project, some rigorous mathematical theories will be attempted to be provided for the solution behaviour of the Boltzmann equation described by some non-classical fluid dynamic systems so that some of these important physical phenomena can be justified by mathematical analysis.