Solving Landau equation for some soft potentials through a probabilistic approach
Guérin, Hélène
Ann. Appl. Probab., Tome 13 (2003) no. 1, p. 515-539 / Harvested from Project Euclid
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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.
Publié le : 2003-05-14
Classification:  Landau equation,  white noise,  nonlinear stochastic differential equation,  nonlinear martingale problems,  60H30,  60H10,  82C40 
@article{1050689592,
     author = {Gu\'erin, H\'el\`ene},
     title = {Solving Landau equation for some soft potentials through a probabilistic approach},
     journal = {Ann. Appl. Probab.},
     volume = {13},
     number = {1},
     year = {2003},
     pages = { 515-539},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1050689592}
}

Guérin, Hélène. Solving Landau equation for some soft potentials through a probabilistic approach. Ann. Appl. Probab., Tome 13 (2003) no. 1, pp.  515-539. http://gdmltest.u-ga.fr/item/1050689592/