Vol. 6, No. 1, 2013

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

Volume 17
Issue 10, 3371–3670
Issue 9, 2997–3369
Issue 8, 2619–2996
Issue 7, 2247–2618
Issue 6, 1871–2245
Issue 5, 1501–1870
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

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
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1948-206X (online)
ISSN 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
Some results on scattering for log-subcritical and log-supercritical nonlinear wave equations

Hsi-Wei Shih

Vol. 6 (2013), No. 1, 1–24
Abstract

We consider two problems in the asymptotic behavior of semilinear second order wave equations. First, we consider the x1 × Lx2 scattering theory for the energy log-subcritical wave equation

u = |u|4ug(|u|)

in 1+3, where g has logarithmic growth at 0. We discuss the solution with general (respectively spherically symmetric) initial data in the logarithmically weighted (respectively lower regularity) Sobolev space. We also include some observation about scattering in the energy subcritical case. The second problem studied involves the energy log-supercritical wave equation

u = |u|4ulogα(2 + |u|2) for 0 < α 4 3

in 1+3. We prove the same results of global existence and (x1 x2) × Hx1 scattering for this equation with a slightly higher power of the logarithm factor in the nonlinearity than that allowed in previous work by Tao (J. Hyperbolic Differ. Equ., 4:2 (2007), 259–265).

Keywords
scattering, log-subcritical, radial Sobolev inequality
Mathematical Subject Classification 2010
Primary: 35L15
Milestones
Received: 27 May 2011
Revised: 22 November 2011
Accepted: 20 March 2012
Published: 1 June 2013
Authors
Hsi-Wei Shih
School of Mathematics
University of Minnesota
127 Vincent Hall, 206 Church St. SE
Minneapolis, MN 55455
United States
http://math.umn.edu/~shihx029/