Displaying similar documents to “On the Landau approximation in plasma physics”

Pointwise convergence of Boltzmann solutions for grazing collisions in a Maxwell gas via a probabilitistic interpretation

Hélène Guérin (2004)

ESAIM: Probability and Statistics

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Using probabilistic tools, this work states a pointwise convergence of function solutions of the 2-dimensional Boltzmann equation to the function solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of Fournier (2000) on the Malliavin calculus for the Boltzmann equation. Moreover, using the particle system introduced by Guérin and Méléard (2003), some simulations of the solution of the Landau equation will be given....

The Boltzmann Equation: Mathematics and Applications

Carlo Cercignani (2007)

Bollettino dell'Unione Matematica Italiana

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The paper is subdivided into two parts. The first presents a recent result by the author concerning the existence of the solution of the Boltzmann equation for Maxwell molecules, without any cutoff in the collision kernel, when the solution depends on just one variable. At variance with the well-known theorem of DiPerna- Lions, conservation of energy is also shown to hold. The second part will concern rarefied gas dynamics problems, governed by the Boltzmann equation and con- cerning...

Kinetic and hydrodynamic equations for granular media

Mario Pulvirenti (1999)

Journées équations aux dérivées partielles

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In this lecture i present some open mathematical problems concerning some PDE arising in the study of one-dimensional models for granular media.