Low regularity for a quadratic Schrödinger equation on the circle

Details Low regularity for a quadratic Schrödinger equation on the circle Low regularity for a quadratic Schrödinger equation on the circle

2008-10-26

arxiv.org/abs/0810.4691v1

Mathematics

Analysis of PDEs

23 pages, 0 figure

Scientific paper

In this paper we consider a Schrodinger equation on the circle with a
quadratic nonlinearity. Thanks to an explicit computation of the first Picard
iterate, we give a precision on the dynamic of the solution, whose existence
was proved by C. E. Kenig, G. Ponce and L. Vega. We also show that the equation
is well-posed in a space based on Lp norms in frequencies.

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