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Article Dans Une Revue Journal of Functional Analysis Année : 2022

Probabilistic local well-posedness for the Schrödinger equation posed for the Grushin Laplacian

Résumé

We study the local well-posedness of the nonlinear Schrödinger equation associated to the Grushin operator with random initial data. To the best of our knowledge, no wellposedness result is known in the Sobolev spaces H k when k 3 2. In this article, we prove that there exists a large family of initial data such that, with respect to a suitable randomization in H k , k ∈ (1, 3 2 ], almost-sure local well-posedness holds. The proof relies on bilinear and trilinear estimates.
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Dates et versions

hal-04196603 , version 1 (05-09-2023)

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Louise Gassot, Mickaël Latocca. Probabilistic local well-posedness for the Schrödinger equation posed for the Grushin Laplacian. Journal of Functional Analysis, 2022, 283 (3), pp.109519. ⟨10.1016/j.jfa.2022.109519⟩. ⟨hal-04196603⟩
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