Kato-type estimates for NLS equation in a scalar field and unique solvability of NKGS system in energy space

Qi-Hong Shi,Wan-Tong Li,Shu Wang

doi:10.1016/j.jde.2014.01.035

Kato-type estimates for NLS equation in a scalar field and unique solvability of NKGS system in energy space

Qi-Hong Shi, Wan-Tong Li + Show 1 more

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https://doi.org/10.1016/j.jde.2014.01.035

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Journal: Journal of Differential Equations	Publication Date: Mar 3, 2014
Citations: 9	License type: publisher-specific-oa

Affiliation: Lanzhou University, Hebei Finance University, Beijing University of Technology

#Equation In R2 #Energy Space + Show 8 more

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Abstract

We consider Schrödinger equation in R2+1 with nonlinear scalar potential. The potentials are time-independent or determined as solutions to inhomogeneous wave equations. By constructing a modified propagator, we derive Kato-type smoothing estimates for the nonlinear Schrödinger (NLS) equation. With the help of these results, we prove the unique solvability of the nonlinear Klein–Gordon–Schrödinger (NKGS) system for all time in the energy space.

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