Vol. 11, No. 5, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 8, 1891–2146
Issue 7, 1643–1890
Issue 7, 1397–1644
Issue 6, 1397–1642
Issue 5, 1149–1396
Issue 4, 867–1148
Issue 3, 605–866
Issue 2, 259–604
Issue 1, 1–258

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
Well-posedness and smoothing effect for generalized nonlinear Schrödinger equations

Pierre-Yves Bienaimé and Abdesslam Boulkhemair

Vol. 11 (2018), No. 5, 1241–1284
Abstract

We improve the result obtained by one of the authors, Bienaimé (2014), and establish the well-posedness of the Cauchy problem for some nonlinear equations of Schrödinger type in the usual Sobolev space Hs(n) for s > n 2 + 2 instead of s > n 2 + 3. We also improve the smoothing effect of the solution and obtain the optimal exponent.

Keywords
Cauchy problem, well-posedness, smoothing effect, nonlinear equation, Schrödinger, paradifferential, pseudodifferential, operator, paralinearization
Mathematical Subject Classification 2010
Primary: 47G20, 47G30
Milestones
Received: 20 June 2017
Revised: 26 November 2017
Accepted: 2 January 2018
Published: 11 April 2018
Authors
Pierre-Yves Bienaimé
Laboratoire de Mathématiques Jean Leray
CNRS UMR6629, Université de Nantes
Nantes
France
Abdesslam Boulkhemair
Laboratoire de Mathématiques Jean Leray
CNRS UMR6629, Université de Nantes
Nantes
France