Low-regularity global well-posedness for the Klein-Gordon-Schr\"odinger system on $\mathbb R^{+}$

E. Compaan; N. Tzirakis

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arXiv · 1803.05057

Low-regularity global well-posedness for the Klein-Gordon-Schr\"odinger system on $\mathbb R^{+}$

E. Compaan·N. Tzirakis

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Abstract

In this paper we establish an almost optimal well-posedness and regularity theory for the Klein-Gordon-Schr\"odinger system on the half line. In particular we prove local-in-time well-posedness for rough initial data in Sobolev spaces of negative indices. Our results are consistent with the sharp well-posedness results that exist in the full line case and in this sense appear to be sharp. Finally we prove a global well-posedness result by combining the $L^2$ conservation law of the Schr\"odinger part with a careful iteration of the rough wave part in lower order Sobolev norms.

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BibTeX RIS

E. Compaan, N. Tzirakis. 2018-03-13. Low-regularity global well-posedness for the Klein-Gordon-Schr\"odinger system on $\mathbb R^{+}$. https://arxiv.org/abs/1803.05057

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