Solving Landau Equation for Some Soft Potentials Through a Probabilistic Approach
This article deals with a way to solve the spatially homogeneous Landau equation using probabilistic tools. Thanks to the study of a nonlinear stochastic differential equation driven by a space-time white noise, we state the existence of a measure solution of the Landau equation with probability mea...
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Veröffentlicht in: | The Annals of applied probability 2003-05, Vol.13 (2), p.515-539 |
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Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | This article deals with a way to solve the spatially homogeneous Landau equation using probabilistic tools. Thanks to the study of a nonlinear stochastic differential equation driven by a space-time white noise, we state the existence of a measure solution of the Landau equation with probability measure initial data, for a generalization of the Maxwellian molecules case. Then, by approximation of the Landau coefficients, the first result helps us to state the existence of a measure solution for some soft potentials [γ ϵ (-1, 0)]. This second part is based on the use of nonlinear stochastic differential equations and some martingale problems. |
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ISSN: | 1050-5164 2168-8737 |
DOI: | 10.1214/aoap/1050689592 |