Remarks on a dispersive equation in de Sitter spacetime

Makoto Nakamura

doi:10.3934/proc.2015.0901

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2015, Volume 2015: 901-905. Doi: 10.3934/proc.2015.0901 open access

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Remarks on a dispersive equation in de Sitter spacetime

Makoto Nakamura^1,

1.
Faculty of Science, Yamagata University, Kojirakawa-machi 1-4-12, Yamagata 990-8560

Received: August 31, 2014

Revised: January 31, 2015

Published: October 2015

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Abstract

Some nonlinear Schrödinger equations are derived from the nonrelativistic limit of nonlinear Klein-Gordon equations in de Sitter spacetime. Time local solutions for the Cauchy problem are considered in Sobolev spaces for power type nonlinear terms. The roles of spatial expansion and contraction on the problem are studied.

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Mathematics Subject Classification: Primary: 35Q55; Secondary: 35L70.

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References

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