Global Newtonian limit for the Relativistic Boltzmann Equation near Vacuum

We study the Cauchy Problem for the relativistic Boltzmann equation with near Vacuum initial data. Unique global in time "mild" solutions are obtained uniformly in the speed of light parameter $c \ge 1$. We furthermore prove that solutions to the relativistic Boltzmann equation converge to solutions of the Newtonian Boltzmann equation in the limit as $c\to\infty$ on arbitrary time intervals $[0,T]$, with convergence rate $1/c^{2-\epsilon}$ for any $\epsilon \in(0,2)$. This may be the first proof of unique global in time validity of the Newtonian limit for a Kinetic equation.Comment: 35 page

Momentum Regularity and Stability of the Relativistic Vlasov-Maxwell-Boltzmann System

In the study of solutions to the relativistic Boltzmann equation, their regularity with respect to the momentum variables has been an outstanding question, even local in time, due to the initially unexpected growth in the post-collisional momentum variables which was discovered in 1991 by Glassey & Strauss \cite{MR1105532}. We establish momentum regularity within energy spaces via a new splitting technique and interplay between the Glassey-Strauss frame and the center of mass frame of the relativistic collision operator. In a periodic box, these new momentum regularity estimates lead to a proof of global existence of classical solutions to the two-species relativistic Vlasov-Boltzmann-Maxwell system for charged particles near Maxwellian with hard ball interaction.Comment: 23 pages; made revisions which were suggested by the referee; to appear in Comm. Math. Phy

Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials

In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out sufficiently close in $L^\infty_\ell$. If the initial data are continuous then so is the corresponding solution. We work in the case of a spatially periodic box. Conditions on the collision kernel are generic in the sense of (Dudy{\'n}ski and Ekiel-Je{\.z}ewska, Comm. Math. Phys., 1988); this resolves the open question of global existence for the soft potentials.Comment: 64 page

Hilbert Expansion from the Boltzmann equation to relativistic Fluids

We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local relativistic Maxwellian constructed from a class of solutions to the relativistic Euler equations that includes a large subclass of near-constant, non-vacuum fluid states. In particular, for small Knudsen number, these solutions to the relativistic Boltzmann equation have dynamics that are effectively captured by corresponding solutions to the relativistic Euler equations.Comment: 50 page

Global Solution to the Relativistic Enskog Equation With Near-Vacuum Data

We give two hypotheses of the relativistic collision kernal and show the existence and uniqueness of the global mild solution to the relativistic Enskog equation with the initial data near the vacuum for a hard sphere gas.Comment: 6 page

Torrefied biomass fuels as a renewable alternative to coal in co-firing for power generation

This study aims to assess the torrefaction of biomass as alternative renewable energy fuel to coal during co-firing. It was evaluated that torrefaction improves biomass grindability to such an extent that it can be used in coal mills with coal in co-firing without capital intensive modification. Torrefaction of beech wood was performed on a batch scale reactor at three different temperatures (200, 250 and 300 °C) with 30 min of residence time. The chemical structural changes in torrefied biomass were investigated with binding energies and FTIR (Fourier transform infrared) analysis. Monocombustion and co-combustion tests were performed to examine the combustion behaviour regarding flue gas emissions (CO, NOx and SO2) at 0.5, 1.5 and 2.5 m distance from the burner opening along with fly ash analysis. The FTIR and binding energies showed that lignin hardly affected during light torrefaction while hemicellulosic material was significantly depleted. The Hardgrove grindability index (HGI) was calculated with three methods (DIN51742, IFK and ISO). The medium temperature torrefied biomass (MTTB) yields HGI value in the range of 32–37 that was comparable with HGI of El Cerrejon coal (36–41). A slight change in temperature enabled the torrefied beech wood to be co-milled with coal without capital intensive modification and improved grindability. Comparing the combustion behaviour of single fuels, low temperature torrefied biomass (LTTB) produces less amount of NOx (426 mg/m3), CO (0.002 mg/m3) and SO2 (2 mg/m3) as compared MTTB and raw beech wood. In the case of co-combustion, it was found that blending of coal with raw biomass does not show a stable behaviour. However, premixing of 50% of coal with 50% of torrefied biomasses (MTTB and LTTB) gives most stable behaviour and reduces NOx almost 30% and SOx up to almost 50% compared to coal. The fly ash contents analysis proved that K2O contents much decreased during co-firing of coal and torrefied fuels that could cause ash related issues during combustion of raw biomass