Local well-posedness for the quadratic Schrodinger equation in two-dimensional compact manifolds with boundary

Nogueira, Marcelo; Panthee, Mahendra

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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Local well-posedness for the quadratic Schrodinger equation in two-dimensional compact manifolds with boundary

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Author(s):	Nogueira, Marcelo ^[1] ; Panthee, Mahendra ^[1] Total Authors: 2
Affiliation:	^[1] Univ Estadual Campinas, Dept Math, BR-13083859 Campinas, SP - Brazil Total Affiliations: 1
Document type:	Journal article
Source:	SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES; JUL 2021.
Web of Science Citations:	0
Abstract
We consider the quadratic NLS posed on a bidimensional compact Riemannian manifold (M, g) with partial derivative M not equal (null set). Using bilinear and gradient bilinear Strichartz estimates for Schrodinger operators in two-dimensional compact manifolds proved by Jiang (Differ Integral Equ 24(1-2):83-108, 2011) we deduce a new evolution bilinear estimates. Consequently, using Bourgain's spaces, we obtain a local well-posedness result for given data u(0) is an element of H-s (M) whenever s > 2/3 in such manifolds. (AU)

FAPESP's process:	20/14833-8 - Nonlinear dispersive wave models
Grantee:	Mahendra Prasad Panthee
Support Opportunities:	Regular Research Grants

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