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arXiv · 1502.04283

Local well-posedness of the nonlinear Schr\"odinger equations on the sphere for data in modulation spaces

Hideo Takaoka
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Abstract

In this paper we discuss a priori estimates derived from the energy method to the initial value problem for the cubic nonlinear Schr\"odinger on the sphere $S^2$. Exploring suitable a priori estimates, we prove the existence of solution for data whose regularity is $s=1/4$.

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Hideo Takaoka. 2015-02-15. Local well-posedness of the nonlinear Schr\"odinger equations on the sphere for data in modulation spaces. https://arxiv.org/abs/1502.04283

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