Propagation of Gevrey regularity for solutions of Landau equations

By using the energy-type inequality, we obtain, in this paper, the result on propagation of Gevrey regularity for the solution of the spatially homogeneous Landau equation in the cases of Maxwellian molecules and hard potential

Gevrey Regularity for Solution of the Spatially Homogeneous Landau Equation

In this paper, we study the Gevrey class regularity for solutions of the spatially homogeneous Landau equations in the hard potential case and the Maxwellian molecules case

Analytic smoothness effect of solutions for spatially homogeneous Landau equation

In this paper, we study the smoothness effect of Cauchy problem for the spatially homogeneous Landau equation in the hard potential case and the Maxwellian molecules case. We obtain the analytic smoothing effect for the solutions under rather weak assumptions on the initial datum.Comment: 16 page

Analysis of controlled auto-ignition /HCCI combustion in a direct injection gasoline engine with single and split fuel injections

A multi-cycle three-dimensional CFD engine simulation programme has been developed and applied to analyze the Controlled autoignition (CAI) combustion, also known as homogeneous charge compression ignition (HCCI), in a direct injection gasoline engine. CAI operation was achieved through the negative valve overlap method by means of a set of low lift camshafts. In the first part of the paper, the effect of single injection timing on combustion phasing and underlying physical and chemical processes involved was examined through a series of analytical studies using the multi-cycle 3D engine simulation programme. The analyses showed that early injection into the trapped burned gases of a lean-burn mixture during the negative valve overlap period had a large effect on combustion phasing, due to localized heat release and the production of chemically reactive species. As the injection was retarded to the intake stroke, the charge cooling effect tended to slow down the autoignition process. However, further retard of fuel injection to the compression stroke caused the earlier start of main combustion as fuel stratification was produced in the cylinder. In order to optimize the engine performance and engine-out emissions, double injection was investigated by injecting part of the fuel first in the negative valve overlap period and the rest of fuel during the intake or compression strokes. By varying the fueling of each injection, the best engine performance was obtained with the 50/50 fuel injection split ratio, while the lowest total NOx and soot emissions were seen with the optimal split injection ratio of 10/90

The Gevrey Hypoellipticity for linear and non-linear Fokker-Planck equations

In this paper, we study the Gevrey regularity of weak solution for a class of linear and quasilinear Fokker-Planck equations