2,804 research outputs found
Optimal time decay of the non cut-off Boltzmann equation in the whole space
In this paper we study the large-time behavior of perturbative classical
solutions to the hard and soft potential Boltzmann equation without the angular
cut-off assumption in the whole space \threed_x with \DgE. We use the
existence theory of global in time nearby Maxwellian solutions from
\cite{gsNonCutA,gsNonCut0}. It has been a longstanding open problem to
determine the large time decay rates for the soft potential Boltzmann equation
in the whole space, with or without the angular cut-off assumption
\cite{MR677262,MR2847536}. For perturbative initial data, we prove that
solutions converge to the global Maxwellian with the optimal large-time decay
rate of O(t^{-\frac{\Ndim}{2}+\frac{\Ndim}{2r}}) in the
L^2_\vel(L^r_x)-norm for any .Comment: 31 pages, final version to appear in KR
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
The Vlasov-Poisson-Landau System in
For the Landau-Poisson system with Coulomb interaction in , we prove
the global existence, uniqueness, and large time convergence rates to the
Maxwellian equilibrium for solutions which start out sufficiently close.Comment: 50 page
Global Classical Solutions of the Boltzmann Equation with Long-Range Interactions and Soft Potentials
In this work we prove global stability for the Boltzmann equation (1872) with
the physical collision kernels derived by Maxwell in 1866 for the full range of
inverse power intermolecular potentials, with . This
completes the work which we began in (arXiv:0912.0888v1). We more generally
cover collision kernels with parameters and satisfying
in arbitrary dimensions
with . Moreover, we prove rapid convergence as predicted by the
Boltzmann H-Theorem. When , we have exponential time decay
to the Maxwellian equilibrium states. When , our solutions
decay polynomially fast in time with any rate. These results are constructive.
Additionally, we prove sharp constructive upper and lower bounds for the
linearized collision operator in terms of a geometric fractional Sobolev norm;
we thus observe that a spectral gap exists only when , as
conjectured in Mouhot-Strain (2007).Comment: This file has not changed, but this work has been combined with
(arXiv:0912.0888v1), simplified and extended into a new preprint, please see
the updated version: arXiv:1011.5441v
Wind speed statistics for Goldstone, California, anemometer sites
An exploratory wind survey at an antenna complex was summarized statistically for application to future windmill designs. Data were collected at six locations from a total of 10 anemometers. Statistics include means, standard deviations, cubes, pattern factors, correlation coefficients, and exponents for power law profile of wind speed. Curves presented include: mean monthly wind speeds, moving averages, and diurnal variation patterns. It is concluded that three of the locations have sufficiently strong winds to justify consideration for windmill sites
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