Vol. 6, No. 4, 2013

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ISSN: 1948-206X (e-only)
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Discrete Fourier restriction associated with KdV equations

Yi Hu and Xiaochun Li

Vol. 6 (2013), No. 4, 859–892
Abstract

In this paper, we consider a discrete restriction associated with KdV equations. Some new Strichartz estimates are obtained. We also establish the local well-posedness for the periodic generalized Korteweg–de Vries equation with nonlinear term F(u)xu provided F C5 and the initial data ϕ Hs with s > 12.

Keywords
discrete Fourier restriction, KdV, local well-posedness
Mathematical Subject Classification 2010
Primary: 35G25
Secondary: 42A16
Milestones
Received: 13 October 2011
Revised: 16 June 2012
Accepted: 21 July 2012
Published: 21 August 2013
Authors
Yi Hu
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, IL 61801
United States
Department of Mathematical Sciences
Georgia Southern University
65 Georgia Ave. Room 3008
Statesboro, GA 30458
United States
Xiaochun Li
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, IL 61801
United States