On the Non-Linear Schrodinger Equation on a Compact Manifold

Abstract : We consider a non-linear Schrodinger equation on a compact manifold of dimension d subject to some multiplicative random perturbation. Using some stochastic Strichartz inequality, we prove the existence and uniqueness of a maximal solution in H1 under some general conditions on the diffusion coefficient. Under stronger conditions on the noise, the nonlinearity and the diffusion coefficient, we deduce the existence of a global solution when d=2. This is a joint work with Z. Brzezniak.
Type de document :
Communication dans un congrès
International Conference on Malliavin Calculus and Stochastic Analysis in Honor of Professor David Nualart, Mar 2011, Lawrence (Kansas), United States. http://www.math.ku.edu/conferences/2011Malliavin/talks.html, 2011
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https://hal.archives-ouvertes.fr/hal-00624308
Contributeur : Annie Millet <>
Soumis le : vendredi 16 septembre 2011 - 13:01:22
Dernière modification le : jeudi 27 avril 2017 - 09:46:16

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  • HAL Id : hal-00624308, version 1

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Annie Millet, Zdzislaw Brzezniak. On the Non-Linear Schrodinger Equation on a Compact Manifold. International Conference on Malliavin Calculus and Stochastic Analysis in Honor of Professor David Nualart, Mar 2011, Lawrence (Kansas), United States. http://www.math.ku.edu/conferences/2011Malliavin/talks.html, 2011. 〈hal-00624308〉

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