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

Marcelo Nogueira; Mahendra Panthee

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arXiv · 1910.12681

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

Marcelo Nogueira·Mahendra Panthee

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Abstract

We consider the quadractic NLS posed on a bidimensional compact Riemannian manifold $(M, g)$ with $ \partial M \neq \emptyset$. Using bilinear and gradient bilinear Strichartz estimates for Schr\"odinger operators in two-dimensional compact manifolds proved by J. Jiang in \cite{JIANG} we deduce a new evolution bilinear estimates. Consequently, using Bourgain's spaces, we obtain a local well-posedness result for given data $u_0\in H^s(M)$ whenever $s> \frac{2}{3}$ in such manifolds.

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Marcelo Nogueira, Mahendra Panthee. 2019-10-28. Local well-posedness for the quadratic Schrodinger equation in two-dimensional compact manifolds with boundary. https://arxiv.org/abs/1910.12681

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