Abstract
We consider the Cauchy problem for the nonlinear Schrödinger equation on \(\mathbb {R}^d\), where the initial data is in \(\dot{H}^1(\mathbb {R}^d)\cap L^p(\mathbb {R}^d)\). We prove local well-posedness for large ranges of p and discuss some global well-posedness results.
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The author was partially suported by Fundação para a Ciência e Tecnologia, through the Grants UID/MAT/04561/2013 and SFRH/BD/96399/2013.
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Correia, S. Local Cauchy theory for the nonlinear Schrödinger equation in spaces of infinite mass. Rev Mat Complut 31, 449–465 (2018). https://doi.org/10.1007/s13163-017-0250-5
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DOI: https://doi.org/10.1007/s13163-017-0250-5