Abstract:
In this paper we consider analyticity in time and smoothing effect of solutions to nonlinear Schrödinger equations
where . We prove that if φ satisfies
then there exists a unique solution of (1) and positive constants T, C 0 , C 1 such that is analytic in time and space variables for and and has an analytic continuation on
and
In the case the condition (2) can be relaxed as follows:
where m= 0 if n= 1, p= 1, m= 1 if n= 2, and m= 1 if n= 3, p= 1.
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Received: 1 March 1994 / Accepted: 16 May 1996
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Hayashi, N., Kato, K. Analyticity in Time and Smoothing Effect of Solutions to Nonlinear Schrödinger Equations . Comm Math Phys 184, 273–300 (1997). https://doi.org/10.1007/s002200050061
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DOI: https://doi.org/10.1007/s002200050061