Global existence of solutions to Schrödinger equations on compact riemannian manifolds below H 1
Bulletin de la Société Mathématique de France, Volume 138 (2010) no. 4, p. 583-613

In this paper, we will study global well-posedness for the cubic defocusing nonlinear Schrödinger equations on the compact Riemannian manifold without boundary, below the energy space, i.e. s<1, under some bilinear Strichartz assumption. We will find some s ˜<1, such that the solution is global for s>s ˜.

Nous nous intéressons dans cet article au caractère bien posé des équations de Schrödinger non-linéaires cubiques défocalisantes sur les variétés riemanniennes compactes sans bord, en régularité H s , s<1, sous certaines conditions bilinéaires de Strichartz. Nous trouvons un s ˜<1 tel que la solution est globale pour s>s ˜.

DOI : https://doi.org/10.24033/bsmf.2597
Classification:  35Q55,  37K05,  37L50,  81Q20
Keywords: schrödinger equation, compact riemannian manifold, global, I-method
@article{BSMF_2010__138_4_583_0,
     author = {Zhong, Sijia},
     title = {Global existence of solutions to Schr\"odinger equations on compact riemannian manifolds below $H^1$},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {138},
     number = {4},
     year = {2010},
     pages = {583-613},
     doi = {10.24033/bsmf.2597},
     zbl = {1236.35002},
     mrnumber = {2794885},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_2010__138_4_583_0}
}
Zhong, Sijia. Global existence of solutions to Schrödinger equations on compact riemannian manifolds below $H^1$. Bulletin de la Société Mathématique de France, Volume 138 (2010) no. 4, pp. 583-613. doi : 10.24033/bsmf.2597. http://www.numdam.org/item/BSMF_2010__138_4_583_0/

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