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May 2003 Solving Landau equation for some soft potentials through a probabilistic approach
Hélène Guérin
Ann. Appl. Probab. 13(2): 515-539 (May 2003). DOI: 10.1214/aoap/1050689592

Abstract

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 [$\gamma \in ( -1,0) $]. This second part is based on the use of nonlinear stochastic differential equations and some martingale problems.

Citation

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Hélène Guérin. "Solving Landau equation for some soft potentials through a probabilistic approach." Ann. Appl. Probab. 13 (2) 515 - 539, May 2003. https://doi.org/10.1214/aoap/1050689592

Information

Published: May 2003
First available in Project Euclid: 18 April 2003

zbMATH: 1070.82027
MathSciNet: MR1970275
Digital Object Identifier: 10.1214/aoap/1050689592

Subjects:
Primary: 60H10 , 60H30 , 82C40

Keywords: Landau equation , nonlinear martingale problems , nonlinear stochastic differential equation , White noise

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.13 • No. 2 • May 2003
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